Find the general solution of the following differential equation y ″ + y ′ = x + 1 Big one, high number, do the right score,

Find the general solution of the following differential equation y ″ + y ′ = x + 1 Big one, high number, do the right score,

The characteristic equation corresponding to homogeneous equation is R & sup2; + r = 0, the characteristic root is r = 0, R2 = - 1, the general solution of homogeneous equation is y = C1 + c2e ^ (- x) and 0 is the characteristic root of equation. Let its special solution be y * = x (AX + b) with 2aX + (a + b) = x + 1, the special solution of solution a = 1 / 2, B = 1 / 2 be y * = (1 / 2) x (x + 1), and the general solution of non-homogeneous equation be y = y + y * = C1