What is the solution for y^{''}-8y^'+16y=16x+5 ?

The solution for y^{''}-8y^'+16y=16x+5 is y=c_{1}e^{4x}+c_{2}xe^{4x}+x+13/16

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y^{''}-8y^'+16y=16x+5

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 x + 5

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + x + \frac{13}{16}

Solution steps

y^{''} (x) - 8 y^{'} (x) + 16 y = 16 x + 5

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + x + \frac{13}{16}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + x + \frac{13}{16}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = \frac{e ^{t}}{t}

y^{^{''}} - 2 y^{^{'}} - 15 y = 3 e^{5 t}

y^{^{'''}} + 4 y^{^{''}} - 5 y = x e^{x} + 8

y^{^{''}} - 12 y^{^{'}} + 36 y = e^{6 t} arctan (t)

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}-8y^'+16y=16x+5 ?
The solution for y^{''}-8y^'+16y=16x+5 is y=c_{1}e^{4x}+c_{2}xe^{4x}+x+13/16