# GATE Questions & Answers of Higher order linear differential equations

## What is the Weightage of Higher order linear differential equations in GATE Exam?

Total 5 Questions have been asked from Higher order linear differential equations topic of Differential equations subject in previous GATE papers. Average marks 1.40.

If the characteristic equation of the differential equation

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

has two equal roots, then the values of $\alpha$ are

If a and b are constants, the most general solution of the differential equation

$\frac{{d}^{2}x}{d{t}^{2}}+2\frac{dx}{dt}+x=0$ is

With initial values y(0)=y′(0)=1, the solution of the differential equation

$\frac{{d}^{2}y}{d{x}^{2}}+4\frac{dy}{dx}+4y=0$

at x=1 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

 (A) –2 (B) –1 (C) 0 (D) 1

The order of the differential equation $\frac{{d}^{2}\mathrm{y}}{d{\mathrm{t}}^{2}}+{\left(\frac{d\mathrm{y}}{d\mathrm{t}}\right)}^{3}+{\mathrm{y}}^{4}={\mathrm{e}}^{-\mathrm{t}}$ is