What is the solution for x^{''}-x^'-6x=5t ?

The solution for x^{''}-x^'-6x=5t is x=c_{1}e^{3t}+c_{2}e^{-2t}-(5t)/6+5/36

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x^{''}-x^'-6x=5t

x^{^{''}} - x^{^{'}} - 6 x = 5 t

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{5 t}{6} + \frac{5}{36}

Solution steps

x^{''} (t) - x^{'} (t) - 6 x = 5 t

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{5 t}{6} + \frac{5}{36}

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{5 t}{6} + \frac{5}{36}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 7 e x

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{- t}

y^{^{''}} - y^{^{'}} + 4 y = x^{3} e^{2 x} + x e^{2 x}

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

9 y^{^{''}} + 6 y^{^{'}} + y = x^{2}

What is the solution for x^{''}-x^'-6x=5t ?
The solution for x^{''}-x^'-6x=5t is x=c_{1}e^{3t}+c_{2}e^{-2t}-(5t)/6+5/36