1
GATE ME 2024
Numerical
+2
-1.33

If $x(t)$ satisfies the differential equation

$t \frac{dx}{dt} + (t - x) = 0$

subject to the condition $x(1) = 0$, then the value of $x(2)$ is __________ (rounded off to 2 decimal places).

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 __________.
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 _______.
4
GATE ME 2014 Set 2
+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
$$\tan \left( {{{x + y} \over 2}} \right) = x + c$$
GATE ME Subjects
EXAM MAP
Medical
NEET