GATE EE 2026 | Differential Equations Question 1 | Engineering Mathematics

GATE EE 2026

MCQ (Single Correct Answer)

-0

Consider the second-order differential equation

$$ \frac{d^2 y}{d x^2}+\frac{d y}{d x}+y=0 $$

with initial conditions

$$ y(0)=1,\left.\frac{d y}{d x}\right|_{x=0}=1 $$

The solution is given by

$y(x)=\exp \left(-\frac{x}{2}\right)\left(\cos \left(\frac{\sqrt{3} x}{2}\right)+\sqrt{3} \sin \left(\frac{\sqrt{3} x}{2}\right)\right)$

$y(x)=\exp \left(-\frac{x}{2}\right)\left(\cos \left(\frac{\sqrt{3} x}{2}\right)+\frac{1}{\sqrt{3}} \sin \left(\frac{\sqrt{3} x}{2}\right)\right)$

$y(x)=\exp \left(-\frac{x}{2}\right)\left(\cos \left(\frac{\sqrt{3} x}{2}\right)-\frac{1}{\sqrt{3}} \sin \left(\frac{\sqrt{3} x}{2}\right)\right)$

$y(x)=\exp \left(-\frac{x}{2}\right)\left(\cos \left(\frac{\sqrt{3} x}{2}\right)-\sqrt{3} \sin \left(\frac{\sqrt{3} x}{2}\right)\right)$

GATE EE 2025

Numerical

-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).

Your input ____

GATE EE 2024

MCQ (More than One Correct Answer)

-0

Which of the following differential equations is/are nonlinear?

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

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

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

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

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

-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

$$(-2, 2)$$

$$(-10, 10)$$

$$(-10, 2)$$

$$(0, 10)$$