What is the solution for y^{''}-7y^'+12y=5x-8 ?

The solution for y^{''}-7y^'+12y=5x-8 is y=c_{1}e^{4x}+c_{2}e^{3x}+(5x)/(12)-61/144

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y^{''}-7y^'+12y=5x-8

y^{^{''}} - 7 y^{^{'}} + 12 y = 5 x - 8

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{5 x}{12} - \frac{61}{144}

Solution steps

y^{''} (x) - 7 y^{'} (x) + 12 y = 5 x - 8

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{5 x}{12} - \frac{61}{144}

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{5 x}{12} - \frac{61}{144}

y^{^{''}} + y = 10 sin (2 t) + 7 t cos (2 t)

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 e^{5 x}

y^{^{''}} + 8 y^{^{'}} + 16 y = - 5 x e^{- 3 x} + 3 e^{- 4 x} - 4

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

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

What is the solution for y^{''}-7y^'+12y=5x-8 ?
The solution for y^{''}-7y^'+12y=5x-8 is y=c_{1}e^{4x}+c_{2}e^{3x}+(5x)/(12)-61/144