What is the solution for y^{''}-y^'-6y=15e^{3t},y(0)=2,y^'(0)=-6 ?

The solution for y^{''}-y^'-6y=15e^{3t},y(0)=2,y^'(0)=-6 is y=-e^{3t}+3e^{-2t}+3e^{3t}t

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y^{''}-y^'-6y=15e^{3t},y(0)=2,y^'(0)=-6

y^{^{''}} - y^{^{'}} - 6 y = 15 e^{3 t}, y (0) = 2, y^{^{'}} (0) = - 6

y = - e^{3 t} + 3 e^{- 2 t} + 3 e^{3 t} t

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = 15 e^{3 t}

Solve linear ODE:

y = - e^{3 t} + 3 e^{- 2 t} + 3 e^{3 t} t

y = - e^{3 t} + 3 e^{- 2 t} + 3 e^{3 t} t

What is the solution for y^{''}-y^'-6y=15e^{3t},y(0)=2,y^'(0)=-6 ?
The solution for y^{''}-y^'-6y=15e^{3t},y(0)=2,y^'(0)=-6 is y=-e^{3t}+3e^{-2t}+3e^{3t}t