What is the solution for (D-2)^2y=20-3xe^2x ?

The solution for (D-2)^2y=20-3xe^2x is y=c_{1}e^{2x}+c_{2}xe^{2x}-(3e^2x^2)/4-(3e^2x)/2+(40-9e^2)/8

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(D-2)^2y=20-3xe^2x

(D - 2)^{2} y = 20 - 3 x e^{2} x

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{3 e ^{2} x ^{2}}{4} - \frac{3 e ^{2} x}{2} + \frac{40 - 9 e ^{2}}{8}

Solution steps

(D - 2)^{2} y = 20 - 3 x e^{2} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{3 e ^{2} x ^{2}}{4} - \frac{3 e ^{2} x}{2} + \frac{40 - 9 e ^{2}}{8}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{3 e ^{2} x ^{2}}{4} - \frac{3 e ^{2} x}{2} + \frac{40 - 9 e ^{2}}{8}

y^{^{''}} - y^{^{'}} - 15 = 0

y^{^{''}} - y^{^{'}} + 3 y = 9 t + 2

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 sin^{2} (x)

y^{^{''}} - 6 y^{^{'}} + 30 y = 15 sin (x)

y^{^{''}} - π^{2} y = - \frac{1}{π}, y (0) = 0, y (1) = 0

What is the solution for (D-2)^2y=20-3xe^2x ?
The solution for (D-2)^2y=20-3xe^2x is y=c_{1}e^{2x}+c_{2}xe^{2x}-(3e^2x^2)/4-(3e^2x)/2+(40-9e^2)/8