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NIELIT 2018-22

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Arjun asked Dec 7, 2018
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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 $-4$ $4$ $-1$ $1$
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$$1$
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Arjun asked Dec 7, 2018
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The general solution of the differential equation $\frac{dy}{dx} = (1+y^2)(e^{-x^2}-2x \tan^{-1} y)$ is: $e^{x^2} \tan^{-1} y = x+c$ $e^{-x^2} \tan^y = x+c$ $e^x \tan y = x^2+c$ $e^{-x} \tan^{-1} y = x^3+c$
The general solution of the differential equation $\frac{dy}{dx} = (1+y^2)(e^{-x^2}-2x \tan^{-1} y)$ is:$e^{x^2} \tan^{-1} y = x+c$$e^{-x^2} \tan^y = x+c$$e^x \tan y = x^...
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Arjun asked Dec 7, 2018
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The general solution of the partial differential equation $(D^2-D’^2-2D+2D’)Z=0$ where $D= \frac{\partial}{\partial x}$ and $D’=\frac{\partial}{\partial y}$: $f(y+x)+e^{2x}g(y-x)$ $e^{2x} f(y+x)+g(y-x)$ $e^{-2x} f(y+x)+g(y-x)$ $f(y+x)+e^{-2x}g(y-x)$
The general solution of the partial differential equation $(D^2-D’^2-2D+2D’)Z=0$ where $D= \frac{\partial}{\partial x}$ and $D’=\frac{\partial}{\partial y}$:$f(y+x)...
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Arjun asked Dec 7, 2018
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The value of $\int_c \frac{2x^2-5}{(x+2)^2 (x^2+4)x^2}dx$, (where $c$ is the square with vertices $1+i, 2+i, 2+2i, i+2i$) is: $0$ $\pi i$ $2 \pi i$ $4 \pi i$
The value of $\int_c \frac{2x^2-5}{(x+2)^2 (x^2+4)x^2}dx$, (where $c$ is the square with vertices $1+i, 2+i, 2+2i, i+2i$) is:$0$$\pi i$$2 \pi i$$4 \pi i$
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