Help Thrid second and first order differential equation

[klovely]

Help! Thrid second and first order differential equation!

I have no idea how to accomplish this problem. If anyone knows help please help me solve this example before I take my test!

Solve
y''' - y'' - y' + y - x = 0

 

[HallsofIvy]

Have you never taken a course in differential equations? If not I wonder why you would be trying to solve an equation like this. If you have, this should be relatively easy. It is a "linear equation with constant coefficients". The associated homogeneous equation is y'''- y''- y'+ y= 0 which has characteristic equation $r^3- r^2- r+ 1= 0$. An obvious solution to that is r= 1 and then you can divide by r- 1 to get a quadratic equation to solve for the other two roots.

To find a specific solution to the entire equation, try y(x)= Ax+ B for some numbers A and B.