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}

y^{^{''}} + 2 y^{^{'}} + 5 y = 45, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} + y^{^{'}} - 20 y = e^{x} (82 + 84 x - 36 x^{2})

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 8 y = H (t)

(D - 1) (D - 2) (D - 3) y = 6 e^{4 x}

x^{^{''}} + x - 6 = 0

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