What is the solution for y^{''}-y^'-6y=0,y(0)=0,y^'(0)=4 ?

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

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y^{''}-y^'-6y=0,y(0)=0,y^'(0)=4

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 0, y^{^{'}} (0) = 4

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

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = 0

Solve linear ODE:

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

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

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