1
GATE EE 2024
MCQ (More than One Correct Answer)
+2
-0

Which of the following differential equations is/are nonlinear?

A

$t \, x(t) + \frac{dx(t)}{dt} = t^2 e^t$, $x(0) = 0$

B

$\frac{1}{2} e^t + x(t) \frac{dx(t)}{dt} = 0$, $x(0) = 0$

C

$x(t) \cos t - \frac{dx(t)}{dt} \sin t = 1$, $x(0) = 0$

D

$x(t) + e^{\left(\frac{dx(t)}{dt}\right)} = 1$, $x(0) = 0$

2
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the differential equation $$\left( {{t^2} - 81} \right){{dy} \over {dt}} + 5ty = \sin \left( t \right)\,\,$$ with $$y\left( 1 \right) = 2\pi .$$ There exists a unique solution for this differential equation when $$t$$ belongs to the interval
A
$$(-2, 2)$$
B
$$(-10, 10)$$
C
$$(-10, 2)$$
D
$$(0, 10)$$
3
GATE EE 2016 Set 2
Numerical
+2
-0
Let $$y(x)$$ be the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\,\,$$ with initial conditions $$y(0)=0$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = 1.\,\,$$ Then the value of $$y(1)$$ is __________.
Your input ____
4
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A function $$y(t),$$ such that $$y(0)=1$$ and $$\,y\left( 1 \right) = 3{e^{ - 1}},\,\,$$ is a solution of the differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ Then $$y(2)$$ is
A
$$5{e^{ - 1}}$$
B
$$5{e^{ - 2}}$$
C
$$7{e^{ - 1}}$$
D
$$7{e^{ - 2}}$$
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