Question

What is the general form of the general solution of a non-homogeneous DE (uh(t)= general solution of the homogeneous equation, up(t)= any particular solution of the non-homogeneous equation)?

(a) u(t)=uh (t)/up (t)

(b) u(t)=uh (t)*up (t)

(c) u(t)=uh (t)+up (t)

(d) u(t)=uh (t)-up (t)

I have been asked this question in an interview for job.

Question is from Non-Homogeneous Linear PDE with Constant Coefficient topic in section Partial Differential Equations of Engineering Mathematics

Answer 1

Right choice is (c) u(t)=uh (t)+up (t)

To elaborate: The general solution of an inhomogeneous ODE has the general form:  u(t)=uh (t)+up (t), where uh (t) is the general solution of the homogeneous equation, up (t) is any particular solution of the non-homogeneous equation.