1
GATE EE 2025
Numerical
+2
-0
Consider ordinary differential equations given by $\dot{x}_1(t)=2 x_2(t), \dot{x}_2(t)=r(t)$ with initial conditions $x_1(0)=1$ and $x_2(0)=0$. If $r(t)=\left\{\begin{array}{ll}1, & t \geq 0 \\ 0, & t<0\end{array}\right.$, then $t=1, x_1(t)=$ _____________ (Round off to the nearest integer).
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2
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

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

3
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
$$(0, 10)$$
4
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 __________.
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