Recent questions tagged differential-equation

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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)$
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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)$
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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
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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)$$\frac{2}{\sqrt{3}} (...
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The differential equation of the system of circles touching the $y$-axis at the origin is$x^2+y^2-2xy \frac{dy}{dx}=0$$x^2+y^2+2xy \frac{dy}{dx}=0$$x^2-y^2-2xy \frac{dy}{...
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The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)$x^{2}-y^{2}=C$$2x^{2}-y^{2}=C$$2y^{2}-x^{2}=C$$x^...
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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)$$y=y...
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Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is$x^{2}+(y-5)^{2}=25$$x^{2}+y^{2}=100$...
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The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ hasunique solutionno solutioninfinite number of solutionsnone of these
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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 − \...
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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$$1$
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The general solution of the differential equation $\frac{dy}{dx} = (1+y^2)(e^{-x^2}-2x \tan^{-1} y)$ is:$e^{x^2} \tan^{-1} y = x+c$$e^{-x^2} \tan^y = x+c$$e^x \tan y = x^...
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While solving the differential equation $\frac{d^2 y}{dx^2} +4y = \tan 2x$ by the method of variation of parameters, then value of Wronskion (W) is:$1$$2$$3$$4$
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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})$...
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The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $$t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$...
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Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable?$x=0$$x=1$$x=2$$x=3$None of the ab...
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