# GATE Questions & Answers of First order equation (linear and nonlinear)

## What is the Weightage of First order equation (linear and nonlinear) in GATE Exam?

Total 5 Questions have been asked from First order equation (linear and nonlinear) topic of Differential equations subject in previous GATE papers. Average marks 1.40.

Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t > 0 , when the forcing function is x(t) and the initial condition is y(0) . If one wishes to modify the system so that the solution becomes -2y(t) for t > 0 , we need to

The solution of the differential equation

 Group I Group II P. $\frac{dy}{dx}=\frac{y}{x}$ 1. Circles Q. $\frac{dy}{dx}=-\frac{y}{x}$ 2. Straight lines R. $\frac{dy}{dx}=\frac{x}{y}$ 3. Hyperbolas S. $\frac{dy}{dx}=-\frac{x}{y}$
Which of the following is a solution to the differential equation $\frac{dx\left(t\right)}{dt}+3x\left(t\right)=0$ ?