List of top Engineering Mathematics Questions on Differential Equations asked in GATE AE

Given \(y=e^{px}\sin(qx)\), where \(p,q\neq 0\) are real, find the value of \[ \frac{d^{2}y}{dx^{2}}-2p\frac{dy}{dx}+(p^{2}+q^{2})y. \]

The acceleration of a body travelling in a straight line is \(a=-C_1-C_2v^2\) where \(v\) is the velocity and \(C_1,C_2 > 0\). Starting with an initial positive velocity \(v_0\), the distance travelled before coming to rest for the first time is:

Solve differential equation: \[ x^2 \frac{d^2y}{dx^2} + 4x \frac{dy}{dx} + 2y = 0, x \geq 1 \] with initial conditions $y=0, \; y'(1)=1$ at $x=1$. Find $y$ at $x=2$. (round off to two decimals)

Consider the equation $\dfrac{dy}{dx} + ay = \sin(\omega x)$, where $a$ and $\omega$ are constants. Given $y=1$ at $x=0$, select all correct statements as $x \to \infty$.