What is the solution for y^{''}+y^'-6y=0,y(0)=2,y^'(0)=-1 ?

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

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y^{''}+y^'-6y=0,y(0)=2,y^'(0)=-1

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

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

Solution steps

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

Solve linear ODE:

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

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

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