Solve ODE with direct integration

[veneficus5]

Homework Statement

Latex takes me forever so I'm going to take a picture

Homework Equations

The Attempt at a Solution

I'm having issues with integrating functions. There seems to be this (x-x0) term that crops up everywhere. Last time it was (t - tau). It's always (variable - dummy variable) so far, but I don't understand why. I also tried plugging it into the original, but I didn't know how to take the derivative of an integral with a mix of dummy and real variables. I guess this is something I should have learned in calculus but never did?

Thanks a lot!

 

[lurflurf]

Recall from elementary calculus the Cauchy formula for repeated integration, which follows from integrationby parts and allows one to write a repeated integral as a single integral. In other words you have found two equivelant ways to express the answer.