GATE ME 2022 Set 2 | Differential Equations Question 5 | Engineering Mathematics

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GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.66

For the exact differential equation,

$\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$

which one of the following is the solution?

u² + 2x² = constant

xu² + u = constant

$\frac{1}{2}x^2u^2+2u$ = constant

$\frac{1}{2}ux^2+2u$ = constant

GATE ME 2017 Set 2

Numerical

-0

Consider the differential equation $$\,\,3y''\left( x \right) + 27y\left( x \right) = 0\,\,$$ with initial conditions $$y\left( 0 \right) = 0$$ and $$y'\left( 0 \right) = 2000.\,\,$$ The value of $$y$$ at $$x=1$$ is __________.

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GATE ME 2016 Set 1

Numerical

-0

If $$y = f(x)$$ satiesfies the boundary value problem $$\,\,y''\,\,\, + \,\,\,9y\,\,\, = \,\,\,0,\,\,\,y\left( 0 \right)\,\,\, = \,\,\,0,\,$$ $$\,\,y\left( {{\pi \over 2}} \right) = \sqrt 2 ,\,\,\,$$ then $$\,\,y\left( {{\pi \over 4}} \right)\,\,$$ is _______.

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GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.6

The matrix form of the linear system $${{dx} \over {dt}} = 3x - 5y$$ and $$\,{{dy} \over {dt}} = 4x + 8y\,\,$$ is

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & { - 5} \cr 4 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & 8 \cr 4 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & { - 5} \cr 3 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & 8 \cr 3 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

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