1
GATE ME 2022 Set 2
MCQ (Single Correct Answer)
+2
-0.66

For the exact differential equation,

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

which one of the following is the solution?

A
u2 + 2x2 = constant
B
xu2 + u = constant
C
$\frac{1}{2}x^2u^2+2u$ =  constant
D
$\frac{1}{2}ux^2+2u$  = constant
2
GATE ME 2017 Set 2
Numerical
+2
-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 __________.
Your input ____
3
GATE ME 2016 Set 1
Numerical
+2
-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 _______.
Your input ____
4
GATE ME 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = \cos \left( {x + y} \right),\,\,$$ with $$c$$ as a constant, is
A
$$y + \sin \left( {x + y} \right) = x + c$$
B
$$\tan \left( {{{x + y} \over 2}} \right) = y + c$$
C
$$\cos \left( {{{x + y} \over 2}} \right) = x + c$$
D
$$\tan \left( {{{x + y} \over 2}} \right) = x + c$$
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