Jawab:

Penjelasan dengan langkah-langkah:

The equation (D^2+D-2)y =x+sinx can be rewritten as (D-1)(D+2)y =x+sinx

equivalent to the system (D+2)y =V(x) , (D-1)V = x+sinx. For the second

quation the integrating factor is e^-x and the solution for V(x) is

V =(e^x)(Integral of (e^-x)(x+sinx)+C1).Obtain

V(x) = (1/2)(sinx+cosx) -(x+1) + C1e^x. Substituting in the first equation of the

above sistem which as the integrating factor e^2x leads to

y =(e^-2x)(Integral of (e^2x)((sinx+cosx)/2 -(x+1) +C1e^3x ) +C2).

Integrating obtain the general integral

y = (C1/3)e^x +C2e^-2x +(3sinx+cosx)/10 -(2x+1)/4.