How do I solve the second order non homogeneous DE x''(t) = e^x -1 ?

Question

How do I solve the second order non homogeneous DE  x''(t) = e^x -1 ?

anonymous · Answer

ok so you would take -1 and add it to e^x then take x" and divide by (t) make sense allen_83?

anonymous · Answer

forget about t . that's the rate of change with respect to time. for $$x'' = e^x$$ there aint no problem. one can apply $$\lambda^2 = 0 $$ and solve for the roots which are in my case 0 (i.e for the hom. part)and for the inhom. part equate the right hand side to $$Ce^x$$ and solve for the constant C which turns out to be 1 and plug C back in and add hom. + inhom. to obtain a genral solution. However the question is what now with this $$e^x -1 $$ ? how do I come up with a hint tosolve this equation ? and your suggestion makes no sense my frined. maybe it's time to start lovin math. ANY ideas ?