What is the solution for (d-2)^2y=3e^2x+5e ?

The solution for (d-2)^2y=3e^2x+5e is y=c_{1}e^{2x}+c_{2}xe^{2x}+(3e^2x)/4+(5e+3e^2)/4

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(d-2)^2y=3e^2x+5e

(d - 2)^{2} y = 3 e^{2} x + 5 e

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 e ^{2} x}{4} + \frac{5 e + 3 e ^{2}}{4}

Solution steps

(d - 2)^{2} y = 3 e^{2} x + 5 e

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 e ^{2} x}{4} + \frac{5 e + 3 e ^{2}}{4}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 e ^{2} x}{4} + \frac{5 e + 3 e ^{2}}{4}

y^{^{'''}} - 3 y^{^{'}} + 2 y = 9 e^{x}

y^{^{''}} - 6 y^{^{'}} + 5 y = 3^{x}

(d^{2} - 4 d + 4) y = x^{2} + e^{x} + cos^{2} (x)

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

(d - 1)^{2} (d^{2} + 1) y = 3 x^{2} - 5 x + 2

What is the solution for (d-2)^2y=3e^2x+5e ?
The solution for (d-2)^2y=3e^2x+5e is y=c_{1}e^{2x}+c_{2}xe^{2x}+(3e^2x)/4+(5e+3e^2)/4