# GATE Questions & Answers of Differential equations Electrical Engineering

#### Differential equations 7 Question(s)

The solution for the differential equation

$\frac{{d}^{2}x}{d{t}^{2}}=-9x,$

with initial conditions $x\left(0\right)=1$ and ${\overline{)\frac{dx}{dt}}}_{t=0}=1$ is

Consider the differential equation ${x}^{2}\frac{{d}^{2}y}{d{x}^{2}}+x\frac{dy}{dx}-y=0$ Which of the following is a solution to this differential equation for x > 0?

With initial condition x(1) = 0.5 , the solution of the differential equation,

$t\frac{dx}{dt}+x=t$ is

Consider the differential equation

$\frac{{d}^{2}y\left(t\right)}{d{t}^{2}}+2\frac{dy\left(t\right)}{dt}+y\left(t\right)=\delta \left(t\right)$ with ${\overline{)y\left(t\right)}}_{t={0}^{-}}=-2$ and ${\overline{)\frac{dy}{dt}}}_{t={0}^{-}}=0$

The numerical value of ${\overline{)\frac{dy}{dt}}}_{t={0}^{+}}$ is

With K as a constant, the possible solution for the first order differential equation $\frac{\mathit{d}y}{\mathit{d}x}={e}^{-3x}$ is

For the differential equation $\frac{{d}^{2}x}{d{t}^{2}}+6\frac{dx}{dt}+8x=0$ with initial conditions x(0) = 1 and ${\overline{)\frac{dx}{dt}}}_{t=0}=0$ the solution is
A differential equation $\frac{dx}{dt}={e}^{-2t}u\left(t\right)$,has to be solved using trapezoidal rule of integration with a step size h=0.01s.Function u(t) indicates a unit step function. If x(0-)=0,then value of x at t=0.01 s will be given by