What is the solution for y^{''}-2y^'=30e^{-3t},y(0)=1,y^'(0)=0 ?

The solution for y^{''}-2y^'=30e^{-3t},y(0)=1,y^'(0)=0 is y=3e^{2t}-4+2e^{-3t}

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y^{''}-2y^'=30e^{-3t},y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

y = 3 e^{2 t} - 4 + 2 e^{- 3 t}

Solution steps

y^{''} (t) - 2 y^{'} (t) = 30 e^{- 3 t}

Solve linear ODE:

y = 3 e^{2 t} - 4 + 2 e^{- 3 t}

y = 3 e^{2 t} - 4 + 2 e^{- 3 t}

What is the solution for y^{''}-2y^'=30e^{-3t},y(0)=1,y^'(0)=0 ?
The solution for y^{''}-2y^'=30e^{-3t},y(0)=1,y^'(0)=0 is y=3e^{2t}-4+2e^{-3t}