What is the solution for y^{''}+y^'-6y=0,y(0)=-3 ?

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

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y^{''}+y^'-6y=0,y(0)=-3

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 3

y = (- 3 - c_{2}) e^{2 t} + c_{2} e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = (- 3 - c_{2}) e^{2 t} + c_{2} e^{- 3 t}

y = (- 3 - c_{2}) e^{2 t} + c_{2} e^{- 3 t}

x^{^{''}} + 6 x^{^{'}} + 3 x = 0, x^{^{'}} (0) = 1, x (0) = 2

y^{^{'''}} + 3 y + 4 y = 0

y^{^{''}} - a y^{^{'}} + y = 0

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 4, y (0) = 2

y^{^{''}} + 2 y^{^{''}} + y = 0

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