What is the solution for y^{''}-9y^'=1+3e^{2x} ?

The solution for y^{''}-9y^'=1+3e^{2x} is y=c_{1}e^{9x}+c_{2}-x/9-3/14 e^{2x}

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y^{''}-9y^'=1+3e^{2x}

y^{^{''}} - 9 y^{^{'}} = 1 + 3 e^{2 x}

y = c_{1} e^{9 x} + c_{2} - \frac{x}{9} - \frac{3}{14} e^{2 x}

Solution steps

y^{''} (x) - 9 y^{'} (x) = 1 + 3 e^{2 x}

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} - \frac{x}{9} - \frac{3}{14} e^{2 x}

y = c_{1} e^{9 x} + c_{2} - \frac{x}{9} - \frac{3}{14} e^{2 x}

What is the solution for y^{''}-9y^'=1+3e^{2x} ?
The solution for y^{''}-9y^'=1+3e^{2x} is y=c_{1}e^{9x}+c_{2}-x/9-3/14 e^{2x}