- 10

- 0

y_p1 = Ce^(-x)

-Ce^(-x) + 3Ce^(-x) - 3Ce^(-x) + Ce^(-x) = e^(-x)

0*Ce^(-x) = e^(-x)

y_p1 = 0

y_p2 = C1 + (C2)x

0 + 3(0) + 3(C2) + C1 + (C2)x = 1 + x

get like terms together so...

(C2)x = x and 3(C2) + C1 = 1 therefore C2 = 1 and C1 = -2

y_p2 = -2 + x

particular solution = y_p1 + y_p2 = -2 + x

and then the general solution to the problem would be:

C1e^(-x) + c2(x)e^(-x) + C3(x^2)e^(-x)