What is the solution for y^{''}-16y^'+64y=(x+1)e^x ?

The solution for y^{''}-16y^'+64y=(x+1)e^x is y=c_{1}e^{8x}+c_{2}xe^{8x}+(e^xx)/(49)+9/343 e^x

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y^{''}-16y^'+64y=(x+1)e^x

y^{^{''}} - 16 y^{^{'}} + 64 y = (x + 1) e^{x}

y = c_{1} e^{8 x} + c_{2} x e^{8 x} + \frac{e ^{x} x}{49} + \frac{9}{343} e^{x}

Solution steps

y^{''} (x) - 16 y^{'} (x) + 64 y = (x + 1) e^{x}

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} x e^{8 x} + \frac{e ^{x} x}{49} + \frac{9}{343} e^{x}

y = c_{1} e^{8 x} + c_{2} x e^{8 x} + \frac{e ^{x} x}{49} + \frac{9}{343} e^{x}

y^{^{''}} - 4 y^{^{'}} + 8 y = x^{3} + x

y^{^{''}} + 4 y = 6 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 3

4 y^{^{''}} - y = 1, y (0) = 0, y^{^{'}} (0) = 0.5

y^{^{''}} + 4 y = 2 x

y^{^{'''}} - 6 y^{^{''}} + 13 y^{^{'}} - 10 y = e^{2 x}

What is the solution for y^{''}-16y^'+64y=(x+1)e^x ?
The solution for y^{''}-16y^'+64y=(x+1)e^x is y=c_{1}e^{8x}+c_{2}xe^{8x}+(e^xx)/(49)+9/343 e^x