What is the solution for y^{''}-18y^'+81y=(x+1)e^x ?

The solution for y^{''}-18y^'+81y=(x+1)e^x is y=c_{1}e^{9x}+c_{2}xe^{9x}+(e^xx)/(64)+5/256 e^x

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y^{''}-18y^'+81y=(x+1)e^x

y^{^{''}} - 18 y^{^{'}} + 81 y = (x + 1) e^{x}

y = c_{1} e^{9 x} + c_{2} x e^{9 x} + \frac{e ^{x} x}{64} + \frac{5}{256} e^{x}

Solution steps

y^{''} (x) - 18 y^{'} (x) + 81 y = (x + 1) e^{x}

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} x e^{9 x} + \frac{e ^{x} x}{64} + \frac{5}{256} e^{x}

y = c_{1} e^{9 x} + c_{2} x e^{9 x} + \frac{e ^{x} x}{64} + \frac{5}{256} e^{x}

4 y^{^{''}} + y = 2 sec (\frac{x}{2})

y^{^{''}} + y^{^{'}} - 12 y = 2 x

y^{^{''}} + 9 y = 9

y^{^{''}} - 5 y^{^{'}} - 6 y = 3 cos (x) + 19 sin (x)

y^{^{''}} - 4 y = 8 x^{2} - 2 x

What is the solution for y^{''}-18y^'+81y=(x+1)e^x ?
The solution for y^{''}-18y^'+81y=(x+1)e^x is y=c_{1}e^{9x}+c_{2}xe^{9x}+(e^xx)/(64)+5/256 e^x