What is the solution for y^{''}-8y^'+16y=20x+7 ?

The solution for y^{''}-8y^'+16y=20x+7 is y=c_{1}e^{4x}+c_{2}xe^{4x}+(5x)/4+17/16

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y^{''}-8y^'+16y=20x+7

y^{^{''}} - 8 y^{^{'}} + 16 y = 20 x + 7

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{5 x}{4} + \frac{17}{16}

Solution steps

y^{''} (x) - 8 y^{'} (x) + 16 y = 20 x + 7

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{5 x}{4} + \frac{17}{16}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{5 x}{4} + \frac{17}{16}

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

y^{^{''}} + 4 y^{^{'}} - 2 y = 2 t^{2} - 3 t + 6

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = x e^{x}

y^{^{'''}} - y^{^{'}} = csc (t)

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

What is the solution for y^{''}-8y^'+16y=20x+7 ?
The solution for y^{''}-8y^'+16y=20x+7 is y=c_{1}e^{4x}+c_{2}xe^{4x}+(5x)/4+17/16