What is the solution for y^{''}-y^'-30y=84e^{2t} ?

The solution for y^{''}-y^'-30y=84e^{2t} is y=c_{1}e^{6t}+c_{2}e^{-5t}-3e^{2t}

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y^{''}-y^'-30y=84e^{2t}

y^{^{''}} - y^{^{'}} - 30 y = 84 e^{2 t}

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

Solution steps

y^{''} (t) - y^{'} (t) - 30 y = 84 e^{2 t}

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = e^{(- t)} ln (t)

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

y^{^{''}} + 9 y = cos (3 t), y (0) = 5, y^{^{'}} (0) = 4

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 t^{2} + 4 + e^{2 t} + t sin (2 t)

y^{^{''}} + 9 y = 4 (\frac{\frac{u ^{5}}{3} π - u ^{13}}{3 π})

What is the solution for y^{''}-y^'-30y=84e^{2t} ?
The solution for y^{''}-y^'-30y=84e^{2t} is y=c_{1}e^{6t}+c_{2}e^{-5t}-3e^{2t}