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 xt=x1t and xt=x2t of the differential equation

d2xtdt2+xt=0,t>0,such that x10=1,dx1tdtt=0=0,x20=0,dx2tdtt=0=1.

The Wronskian Wt=x1tx2tdx1tdtdx2tdt at t=π2  is

The partial differential equation ut+uux=2u 2xis a

The Blasius equation d3fdη3+f2d2fdη2=0 is a

The partial differential equation 2φx2+2φy2+φx+φy=0 has