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 dydx=ky,y0=c is

Match each differential equation in Group I to its family of solution curves from Group II.

  Group I   Group II
P. dydx=yx 1. Circles
Q. dydx=-yx 2. Straight lines
R. dydx=xy 3. Hyperbolas
S. dydx=-xy    

Which of the following is a solution to the differential equation dxtdt+3xt=0 ?