What is the solution for y^{''}+5y^'-6y=0,y(0)=-5,y^'(0)=37 ?

The solution for y^{''}+5y^'-6y=0,y(0)=-5,y^'(0)=37 is y=e^t-6e^{-6t}

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y^{''}+5y^'-6y=0,y(0)=-5,y^'(0)=37

y^{^{''}} + 5 y^{^{'}} - 6 y = 0, y (0) = - 5, y^{^{'}} (0) = 37

y = e^{t} - 6 e^{- 6 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) - 6 y = 0

Solve linear ODE:

y = e^{t} - 6 e^{- 6 t}

y = e^{t} - 6 e^{- 6 t}

y^{^{''}} + 2 y^{^{'}} = - 4 y

y^{^{''}} = y^{^{'}} + y

y^{^{''}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

y^{^{''}} - 9 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 2

u^{^{''}} + 2 u^{^{'}} + 2 H (t) = 0

What is the solution for y^{''}+5y^'-6y=0,y(0)=-5,y^'(0)=37 ?
The solution for y^{''}+5y^'-6y=0,y(0)=-5,y^'(0)=37 is y=e^t-6e^{-6t}