What is the solution for y^{''}+y^'-6y=0,y(0)=-2,y^'(0)=16 ?

The solution for y^{''}+y^'-6y=0,y(0)=-2,y^'(0)=16 is y=2e^{2t}-4e^{-3t}

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y^{''}+y^'-6y=0,y(0)=-2,y^'(0)=16

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

y = 2 e^{2 t} - 4 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{2 t} - 4 e^{- 3 t}

y = 2 e^{2 t} - 4 e^{- 3 t}

v^{^{''}} + v^{^{'}} \cdot 1000 + v \cdot 125000 = 0

y^{^{''}} + 40 y^{^{'}} + 490 y = 0

y^{^{''}} - 3 y^{^{'}} + 1 y = 0

y^{^{''}} - 9 y = 0, y (0) = 3, y^{^{'}} (0) = - 9

y^{^{''}} - 25 y^{^{'}} + 144 y = 0, y^{^{'}} (0) = 5

What is the solution for y^{''}+y^'-6y=0,y(0)=-2,y^'(0)=16 ?
The solution for y^{''}+y^'-6y=0,y(0)=-2,y^'(0)=16 is y=2e^{2t}-4e^{-3t}