What is the solution for y^{''}+2y^'-8y=0,y^'(0)=14 ?

The solution for y^{''}+2y^'-8y=0,y^'(0)=14 is y=(7+2c_{2})e^{2t}+c_{2}e^{-4t}

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y^{''}+2y^'-8y=0,y^'(0)=14

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y^{^{'}} (0) = 14

y = (7 + 2 c_{2}) e^{2 t} + c_{2} e^{- 4 t}

Solution steps

y^{''} (t) + 2 y^{'} (t) - 8 y = 0

Solve linear ODE:

y = (7 + 2 c_{2}) e^{2 t} + c_{2} e^{- 4 t}

y = (7 + 2 c_{2}) e^{2 t} + c_{2} e^{- 4 t}

x^{^{''}} + 2 x^{^{'}} - 8 x = 0

9 y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 2

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

4 y^{^{''}} - 36 y = 0

What is the solution for y^{''}+2y^'-8y=0,y^'(0)=14 ?
The solution for y^{''}+2y^'-8y=0,y^'(0)=14 is y=(7+2c_{2})e^{2t}+c_{2}e^{-4t}