What is the solution for y^{''}+y^'-12y=2x ?

The solution for y^{''}+y^'-12y=2x is y=c_{1}e^{3x}+c_{2}e^{-4x}-x/6-1/72

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

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

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{x}{6} - \frac{1}{72}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{x}{6} - \frac{1}{72}

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{x}{6} - \frac{1}{72}

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

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

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

y^{^{''}} + 9 y = 1

u^{^{''}} - a \cdot H (x) = x, u^{^{'}} (- 1) = 0, u^{^{'}} (1) = 0

What is the solution for y^{''}+y^'-12y=2x ?
The solution for y^{''}+y^'-12y=2x is y=c_{1}e^{3x}+c_{2}e^{-4x}-x/6-1/72