Answer to Question #161877 in Differential Equations for حسين

Question

(3D ^ 2 + D ^ 2 + D) * Z = X + 5Y

Answer 1

3D²+D²+D=D(4D+1)=0

Roots: 0,-1/4

CF: c₁e⁰+c₂e^-1/4=c₁+c₂e^-1/4

PI: $\frac{x+5y}{4D+1}=\frac{x+5y}{4(D+1/4)}(1)$

$\frac{x+5y}{4} \frac{1}{D} {1/4}=\frac{x+5y}{16}xy$

$z=c_1+c_2e^{-1/4}+\frac{x+5y}{16}xy$