Inhomogenous ODEs, Particular solutions question

[Moham1287]

1.The position of a particle x(t) obeys the following differential equation

d^2x/dt^2 + 4(dx/dt) + 3x = (3t/2) -4

If at t=0, both x=0 and dt/dx=0, find x(t)





Attempt at solution
I've found the homogeneous solution to be y=Aexp(-3x) + Bexp(-x), and know how to find x(t) given boundary conditions, but I'm having trouble finding the particular solution. I know you have to use g(x) where g(x) is the RHS of the equation, but when I try using Yp=r exp(mu x) or a combination of factors of x, I get a load of rubbish. Can anyone please help?

 

[Dick]

If you look at the form of the RHS, you might guess that a particular solution would have the form x(t)=a*t+b. Put that into the equation at try to find a and b. You first try at finding a particular solution should always be to try and guess what it could be and then prove yourself right.