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

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

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y^{''}-5y^'-6y=-6e^t

y^{^{''}} - 5 y^{^{'}} - 6 y = - 6 e^{t}

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

Solution steps

y^{''} (t) - 5 y^{'} (t) - 6 y = - 6 e^{t}

Solve linear ODE:

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

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

y^{^{''}} - 4 y = e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} - 28 y = 1056 e^{- t}

y^{^{''}} + y = g (t), y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} - x = 4 e^{- t}

y^{^{''}} + 6 y^{^{'}} + 18 y = 11 t e^{4 t}

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