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}+5-(e^{2x}x^3)/2

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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} + 5 - \frac{e ^{2 x} x ^{3}}{2}

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} + 5 - \frac{e ^{2 x} x ^{3}}{2}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 5 - \frac{e ^{2 x} x ^{3}}{2}

y^{^{''}} - y = cos^{2} (x)

y^{^{''}} + 16 y = sec (4 t)

y^{^{''}} + 4 y = 3 sin (2 x) + x^{2} - 1

y^{^{''}} + 4 y = cos (x) cos (3 x)

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x}

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}+5-(e^{2x}x^3)/2