If y'''+y''+y'+y=x, what is the function y?

Answer 1

There were no intial conditions given? So, Lets assume that,,,,

y(0) = A, y'(0) = B, y''(0) = C

Then y = (A/2)e^-x + (A/2)cos(x) + (A/2)sin(x) + Bsin(x) + (C/2)e^-x - (C/2)cos(x) + (C/2)sin(x) +

(1/2)e^-x + (1/2)cos(x) - (1/2)sin(x) + x - 1