# GATE Questions & Answers of Higher Order Linear Differential Equations With Constant Coefficients

## What is the Weightage of Higher Order Linear Differential Equations With Constant Coefficients in GATE Exam?

Total 7 Questions have been asked from Higher Order Linear Differential Equations With Constant Coefficients topic of Differential equations subject in previous GATE papers. Average marks 1.43.

Given the ordinary differential equation

$\frac{d^2y}{dx^2}+\frac{dy}{dx}-6y=0$

with $y\left(0\right)=0$ and $\frac{dy}{dx}\left(0\right)=1$ , the value of $y\left(1\right)$ is _________ (correct to two decimal places).

The differential equation $\style{font-family:'Times New Roman'}{\frac{d^2y}{dx^2}+16y=0}$ for $\style{font-family:'Times New Roman'}{y\left(x\right)}$ with the two boundary conditions $\style{font-family:'Times New Roman'}{{\left.\frac{dy}{dx}\right|}_{x-0}=1\;\mathrm{and}\;{\left.\frac{dy}{dx}\right|}_{x-\frac{\mathrm\pi}2}=-1}$ has

Consider the differential equation 3y(x)+27 y (x)=0 with initial conditions y (0)=0 and y’(0)=2000. The value of y at x =1 is___________

Consider two solutions $x\left(t\right)={x}_{1}\left(t\right)$ and $x\left(t\right)={x}_{2}\left(t\right)$ of the differential equation

$\frac{{d}^{2}x\left(t\right)}{d{t}^{2}}+x\left(t\right)=0,t>0,$such that ${x}_{1}\left(0\right)=1,{\overline{)\frac{d{x}_{1}\left(t\right)}{dt}}}_{t=0}=0,{x}_{2}\left(0\right)=0,{\overline{)\frac{d{x}_{2}\left(t\right)}{dt}}}_{t=0}=1.$

The Wronskian $W\left(t\right)=\left|\begin{array}{cc}{x}_{1}\left(t\right)& {x}_{2}\left(t\right)\\ \frac{d{x}_{1}\left(t\right)}{dt}& \frac{d{x}_{2}\left(t\right)}{dt}\end{array}\right|\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$ at is

The partial differential equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\frac{{\partial }^{2}u}{{\partial }^{2}x}$is a

The Blasius equation $\frac{{d}^{3}f}{d{\eta }^{3}}+\frac{f}{2}\frac{{d}^{2}f}{d{\eta }^{2}}=0$ is a
The partial differential equation $\frac{{\partial }^{2}\phi }{\partial {x}^{2}}+\frac{{\partial }^{2}\phi }{\partial {y}^{2}}+\left(\frac{\partial \phi }{\partial x}\right)+\left(\frac{\partial \phi }{\partial y}\right)=0$ has