What is the solution for y^{''}+y^'-6y=20e^t,y(0)=0,y^'(0)=1 ?

The solution for y^{''}+y^'-6y=20e^t,y(0)=0,y^'(0)=1 is y=(-4/5+5)e^{2t}+4/5 e^{-3t}-5e^t

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y^{''}+y^'-6y=20e^t,y(0)=0,y^'(0)=1

y^{^{''}} + y^{^{'}} - 6 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y = (- \frac{4}{5} + 5) e^{2 t} + \frac{4}{5} e^{- 3 t} - 5 e^{t}

Solution steps

y^{''} (t) + y^{'} (t) - 6 y = 20 e^{t}

Solve linear ODE:

y = (- \frac{4}{5} + 5) e^{2 t} + \frac{4}{5} e^{- 3 t} - 5 e^{t}

y = (- \frac{4}{5} + 5) e^{2 t} + \frac{4}{5} e^{- 3 t} - 5 e^{t}

What is the solution for y^{''}+y^'-6y=20e^t,y(0)=0,y^'(0)=1 ?
The solution for y^{''}+y^'-6y=20e^t,y(0)=0,y^'(0)=1 is y=(-4/5+5)e^{2t}+4/5 e^{-3t}-5e^t