What is the solution for y^{''}-9y^'+14y=12-e^x ?

The solution for y^{''}-9y^'+14y=12-e^x is y=c_{1}e^{7x}+c_{2}e^{2x}+6/7-1/6 e^x

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y^{''}-9y^'+14y=12-e^x

y^{^{''}} - 9 y^{^{'}} + 14 y = 12 - e^{x}

y = c_{1} e^{7 x} + c_{2} e^{2 x} + \frac{6}{7} - \frac{1}{6} e^{x}

Solution steps

y^{''} (x) - 9 y^{'} (x) + 14 y = 12 - e^{x}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{2 x} + \frac{6}{7} - \frac{1}{6} e^{x}

y = c_{1} e^{7 x} + c_{2} e^{2 x} + \frac{6}{7} - \frac{1}{6} e^{x}

What is the solution for y^{''}-9y^'+14y=12-e^x ?
The solution for y^{''}-9y^'+14y=12-e^x is y=c_{1}e^{7x}+c_{2}e^{2x}+6/7-1/6 e^x