2nd Order Differential Equations

Hello,

Second order differential equation:

y'' - y = exp[x]

Solving for the complementary function, y_c:

m^2 - 1 = 0

-> m = 1 and m = 0

:. y_c = A*exp[-1] + B*exp[0] = A*exp[-1] + B

Solving for the particular integral, y_p:

Try y = a*exp[x] -> this is a solution of the homogeneous eqn, so multiply the function by x:

y = ax*exp[x]

y' = a*exp[x] + ax*exp[x]

y'' = a*exp[x] + a*exp[x] + ax*exp[x]

Substituting into y'' - y' = x*exp[x], the equation reduces to:

a + a*x = x -> How to work the constant (alpha) out?

Thank you