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Recent questions tagged differential-equation
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NIELIT 2017 OCT Scientific Assistant A (IT) - Section D: 6
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$$e^{-2t}u(t)$$e^{2t}u(t)$$e^{-t}u(t)$$e^{t}u(t)$
admin
391
views
admin
asked
Aug 28, 2020
Calculus
nielit2017oct-assistanta-it
differential-equation
non-gate
+
–
0
votes
0
answers
2
NIELIT 2017 OCT Scientific Assistant A (CS) - Section D: 6
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$$e^{-2t}u(t)$$e^{2t}u(t)$$e^{-t}u(t)$$e^{t}u(t)$
admin
305
views
admin
asked
Aug 28, 2020
Optimization
nielit2017oct-assistanta-cs
non-gate
differential-equation
+
–
0
votes
0
answers
3
NIELIT 2016 MAR Scientist B - Section B: 15
Differential equation, $\dfrac{d^2x}{dt^2}+10\dfrac{dx}{dt}+25x=0$ will have a solution of the form $(C_1+C_2t)e^{-5t}$ $C_1e^{-2t}$ $C_1e^{-5t}+C_2e^{5t}$ $C_1e^{-5t}+C_2e^{2t}$ where $C_1$ and $C_2$ are constants.
Differential equation, $\dfrac{d^2x}{dt^2}+10\dfrac{dx}{dt}+25x=0$ will have a solution of the form $(C_1+C_2t)e^{-5t}$$C_1e^{-2t}$$C_1e^{-5t}+C_2e^{5t}$$C_1e^{-5t}+C_2e^...
admin
306
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
non-gate
differential-equation
+
–
0
votes
1
answer
4
ISI2015-MMA-85
The differential equation of all the ellipses centred at the origin is $y^2+x(y’)^2-yy’=0$ $xyy’’ +x(y’)^2 -yy’=0$ $yy’’+x(y’)^2-xy’=0$ none of these
The differential equation of all the ellipses centred at the origin is$y^2+x(y’)^2-yy’=0$$xyy’’ +x(y’)^2 -yy’=0$$yy’’+x(y’)^2-xy’=0$none of these
Arjun
304
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
ellipse
non-gate
+
–
0
votes
1
answer
5
ISI2015-MMA-87
If $x(t)$ is a solution of $(1-t^2) dx -tx\: dt =dt$ and $x(0)=1$, then $x\big(\frac{1}{2}\big)$ is equal to $\frac{2}{\sqrt{3}} (\frac{\pi}{6}+1)$ $\frac{2}{\sqrt{3}} (\frac{\pi}{6}-1)$ $\frac{\pi}{3 \sqrt{3}}$ $\frac{\pi}{\sqrt{3}}$
If $x(t)$ is a solution of $$(1-t^2) dx -tx\: dt =dt$$ and $x(0)=1$, then $x\big(\frac{1}{2}\big)$ is equal to$\frac{2}{\sqrt{3}} (\frac{\pi}{6}+1)$$\frac{2}{\sqrt{3}} (...
Arjun
382
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
non-gate
+
–
1
votes
1
answer
6
ISI2015-MMA-88
Let $f(x)$ be a given differentiable function. Consider the following differential equation in $y$ $f(x) \frac{dy}{dx} = yf’(x)-y^2.$ The general solution of this equation is given by $y=-\frac{x+c}{f(x)}$ $y^2=\frac{f(x)}{x+c}$ $y=\frac{f(x)}{x+c}$ $y=\frac{\left[f(x)\right]^2}{x+c}$
Let $f(x)$ be a given differentiable function. Consider the following differential equation in $y$ $$f(x) \frac{dy}{dx} = yf’(x)-y^2.$$ The general solution of this equ...
Arjun
283
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
general-solution
non-gate
+
–
1
votes
1
answer
7
ISI2015-MMA-89
Let $y(x)$ be a non-trivial solution of the second order linear differential equation $\frac{d^2y}{dx^2}+2c\frac{dy}{dx}+ky=0,$ where $c<0$, $k>0$ and $c^2>k$. Then $\mid y(x) \mid \to \infty$ as $x \to \infty$ $\mid y(x) \mid \to 0$ as $x \to \infty$ $\underset{x \to \pm \infty}{\lim} \mid y(x) \mid$ exists and is finite none of the above is true
Let $y(x)$ be a non-trivial solution of the second order linear differential equation $$\frac{d^2y}{dx^2}+2c\frac{dy}{dx}+ky=0,$$ where $c<0$, $k>0$ and $c^2>k$. Then$\mi...
Arjun
248
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
non-gate
+
–
0
votes
1
answer
8
ISI2015-MMA-90
The differential equation of the system of circles touching the $y$-axis at the origin is $x^2+y^2-2xy \frac{dy}{dx}=0$ $x^2+y^2+2xy \frac{dy}{dx}=0$ $x^2-y^2-2xy \frac{dy}{dx}=0$ $x^2-y^2+2xy \frac{dy}{dx}=0$
The differential equation of the system of circles touching the $y$-axis at the origin is$x^2+y^2-2xy \frac{dy}{dx}=0$$x^2+y^2+2xy \frac{dy}{dx}=0$$x^2-y^2-2xy \frac{dy}{...
Arjun
308
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
non-gate
+
–
0
votes
0
answers
9
ISI2015-MMA-91
Suppose a solution of the differential equation $(xy^3+x^2y^7)\frac{\mathrm{d} y}{\mathrm{d} x}=1,$ satisfies the initial condition $y(1/4)=1$. Then the value of $\dfrac{\mathrm{d} y}{\mathrm{d} x}$ when $y=-1$ is $\frac{4}{3}$ $- \frac{4}{3}$ $\frac{16}{5}$ $- \frac{16}{5}$
Suppose a solution of the differential equation $$(xy^3+x^2y^7)\frac{\mathrm{d} y}{\mathrm{d} x}=1,$$ satisfies the initial condition $y(1/4)=1$. Then the value of $\dfra...
Arjun
249
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
non-gate
+
–
0
votes
1
answer
10
ISI2016-DCG-67
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}-y^{2}=C$ $2x^{2}-y^{2}=C$ $2y^{2}-x^{2}=C$ $x^{2}+y^{2}=C$
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)$x^{2}-y^{2}=C$$2x^{2}-y^{2}=C$$2y^{2}-x^{2}=C$$x^...
gatecse
260
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
11
ISI2016-DCG-68
The general solution of the differential equation $x+y-x{y}'=0$ is (assuming $C$ as an arbitrary constant of integration) $y=x(\log x+C)$ $x=y(\log y+C)$ $y=x(\log y+C)$ $y=y(\log x+C)$
The general solution of the differential equation $x+y-x{y}'=0$ is (assuming $C$ as an arbitrary constant of integration)$y=x(\log x+C)$$x=y(\log y+C)$$y=x(\log y+C)$$y=y...
gatecse
253
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
12
ISI2016-DCG-69
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y-5)^{2}=25$ $x^{2}+y^{2}=100$ $(x-5)^{2}+y^{2}=125$ $(x-5)^{2}+(y-5)^{2}=50$
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is$x^{2}+(y-5)^{2}=25$$x^{2}+y^{2}=100$...
gatecse
349
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
0
answers
13
ISI2017-DCG-24
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ has unique solution no solution infinite number of solutions none of these
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ hasunique solutionno solutioninfinite number of solutionsnone of these
gatecse
310
views
gatecse
asked
Sep 18, 2019
Others
isi2017-dcg
engineering-mathematics
calculus
non-gate
differential-equation
+
–
0
votes
1
answer
14
ISI2018-MMA-25
The solution of the differential equation $(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is $xy = \log\ x − \log\ y + C$ $xy = \log\ y − \log\ x + C$ $x^2y^2 = 2(\log\ x − \log\ y) + C$ $x^2y^2 = 2(\log\ y − \log\ x) + C$
The solution of the differential equation$(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is$xy = \log\ x − \log\ y + C$$xy = \log\ y − \log\ x + C$$x^2y^2 = 2(\log\ x − \...
akash.dinkar12
545
views
akash.dinkar12
asked
May 11, 2019
Others
isi2018-mma
non-gate
differential-equation
+
–
1
votes
1
answer
15
ISI2019-MMA-18
For the differential equation $\frac{dy}{dx} + xe^{-y}+2x=0$ It is given that $y=0$ when $x=0$. When $x=1$, $\:y$ is given by $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3e}{2} – \frac{1}{4} \bigg)$ $\text{ln} \bigg(\frac{3}{e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{4} \bigg)$
For the differential equation $$\frac{dy}{dx} + xe^{-y}+2x=0$$It is given that $y=0$ when $x=0$. When $x=1$, $\:y$ is given by$\text{ln} \bigg(\frac{3}{2e} – \frac{1}{...
Sayan Bose
4.5k
views
Sayan Bose
asked
May 6, 2019
Others
isi2019-mma
non-gate
engineering-mathematics
calculus
differential-equation
+
–
0
votes
1
answer
16
ISI2019-MMA-6
The solution of the differential equation $\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$ is $x^2 + y^2 = cy$, where $c$ is a constant $x^2 + y^2 = cx$, where $c$ is a constant $x^2 – y^2 = cy$ , where $c$ is a constant $x^2 - y^2 = cx$, where $c$ is a constant
The solution of the differential equation $$\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$$is$x^2 + y^2 = cy$, where $c$ is a constant$x^2 + y^2 = cx$, where $c$ is a constant$x^2 ...
Sayan Bose
1.1k
views
Sayan Bose
asked
May 6, 2019
Calculus
isi2019-mma
non-gate
engineering-mathematics
calculus
differential-equation
+
–
1
votes
1
answer
17
NIELIT 2018-18
If $y^a$ is an integrating factor of the differential equation $2xydx-(3x^2-y^2)dy=0$, then the value of $a$ is $-4$ $4$ $-1$ $1$
If $y^a$ is an integrating factor of the differential equation $2xydx-(3x^2-y^2)dy=0$, then the value of $a$ is$-4$$4$$-1$$1$
Arjun
685
views
Arjun
asked
Dec 7, 2018
Others
nielit-2018
non-gate
differential-equation
+
–
1
votes
0
answers
18
NIELIT 2018-20
The general solution of the differential equation $\frac{dy}{dx} = (1+y^2)(e^{-x^2}-2x \tan^{-1} y)$ is: $e^{x^2} \tan^{-1} y = x+c$ $e^{-x^2} \tan^y = x+c$ $e^x \tan y = x^2+c$ $e^{-x} \tan^{-1} y = x^3+c$
The general solution of the differential equation $\frac{dy}{dx} = (1+y^2)(e^{-x^2}-2x \tan^{-1} y)$ is:$e^{x^2} \tan^{-1} y = x+c$$e^{-x^2} \tan^y = x+c$$e^x \tan y = x^...
Arjun
576
views
Arjun
asked
Dec 7, 2018
Others
nielit-2018
non-gate
differential-equation
+
–
1
votes
1
answer
19
NIELIT 2018-22
While solving the differential equation $\frac{d^2 y}{dx^2} +4y = \tan 2x$ by the method of variation of parameters, then value of Wronskion (W) is: $1$ $2$ $3$ $4$
While solving the differential equation $\frac{d^2 y}{dx^2} +4y = \tan 2x$ by the method of variation of parameters, then value of Wronskion (W) is:$1$$2$$3$$4$
Arjun
3.5k
views
Arjun
asked
Dec 7, 2018
Others
nielit-2018
non-gate
differential-equation
+
–
2
votes
0
answers
20
NIELIT 2018-25
The general solution of the partial differential equation $(D^2-D’^2-2D+2D’)Z=0$ where $D= \frac{\partial}{\partial x}$ and $D’=\frac{\partial}{\partial y}$: $f(y+x)+e^{2x}g(y-x)$ $e^{2x} f(y+x)+g(y-x)$ $e^{-2x} f(y+x)+g(y-x)$ $f(y+x)+e^{-2x}g(y-x)$
The general solution of the partial differential equation $(D^2-D’^2-2D+2D’)Z=0$ where $D= \frac{\partial}{\partial x}$ and $D’=\frac{\partial}{\partial y}$:$f(y+x)...
Arjun
821
views
Arjun
asked
Dec 7, 2018
Others
nielit-2018
non-gate
differential-equation
partial-order
+
–
0
votes
1
answer
21
ISI2017-MMA-9
A function $y(x)$ that satisfies $\dfrac{dy}{dx}+4xy=x$ with the boundary condition $y(0)=0$ is $y(x)=(1-e^x)$ $y(x)=\frac{1}{4}(1-e^{-2x^2})$ $y(x)=\frac{1}{4}(1-e^{2x^2})$ $y(x)=\frac{1}{4}(1-\cos x)$
A function $y(x)$ that satisfies $\dfrac{dy}{dx}+4xy=x$ with the boundary condition $y(0)=0$ is$y(x)=(1-e^x)$$y(x)=\frac{1}{4}(1-e^{-2x^2})$$y(x)=\frac{1}{4}(1-e^{2x^2})$...
go_editor
535
views
go_editor
asked
Sep 15, 2018
Calculus
isi2017-mmamma
calculus
differential-equation
non-gate
+
–
0
votes
0
answers
22
ISI2016-MMA-7
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$ is $\{1\}$ $\{1, -1\}$ $\{1, 2\}$ $\{-1, 2\}$
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $$t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$...
go_editor
208
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
differential-equation
non-gate
+
–
0
votes
0
answers
23
virtual gate
Manoja Rajalakshmi A
376
views
Manoja Rajalakshmi A
asked
Nov 17, 2017
Calculus
differential-equation
+
–
8
votes
2
answers
24
TIFR CSE 2012 | Part A | Question: 15
Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable? $x=0$ $x=1$ $x=2$ $x=3$ None of the above
Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable?$x=0$$x=1$$x=2$$x=3$None of the ab...
makhdoom ghaya
1.8k
views
makhdoom ghaya
asked
Oct 30, 2015
Calculus
tifr2012
calculus
differential-equation
+
–
5
votes
1
answer
25
GATE CSE 1993 | Question: 01.2
The differential equation $\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0$ is: linear non- linear homogeneous of degree two
The differential equation $\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0$ is:linearnon- linear ...
Kathleen
1.6k
views
Kathleen
asked
Sep 13, 2014
Calculus
gate1993
calculus
differential-equation
easy
out-of-gate-syllabus
multiple-selects
+
–
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