Please solve the following question. Please do not paste solutions that were already posted on coursehero or on chegg. Please use your own solution.

1.) Find x(t) = _k>=0a_kt^ksuch that x'' = tx + 1 and x(0) = 0, x'(0) = 1

The answer for question 1 when solving the problem should be

x = t + (_n>=1of ((t³ⁿ⁺¹/ ((3n+1)3n(3n-2)(3n-3)....4*3))) + ((t^2)/(2)) + (_n>=1of ((t³ⁿ⁺²/ ((3n+2)(3n+1)(3n-1)(3n-2)....5*4*2)))