What is the solution for y^{''}+5y^'-14y=0,y^'(0)=56 ?

The solution for y^{''}+5y^'-14y=0,y^'(0)=56 is y=(e^{2t}(56+7c_{2}))/2+c_{2}e^{-7t}

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y^{''}+5y^'-14y=0,y^'(0)=56

y^{^{''}} + 5 y^{^{'}} - 14 y = 0, y^{^{'}} (0) = 56

y = \frac{e ^{2 t} ( 56 + 7 c _{2} )}{2} + c_{2} e^{- 7 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) - 14 y = 0

Solve linear ODE:

y = \frac{e ^{2 t} ( 56 + 7 c _{2} )}{2} + c_{2} e^{- 7 t}

y = \frac{e ^{2 t} ( 56 + 7 c _{2} )}{2} + c_{2} e^{- 7 t}

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y^{^{'}} (0) = 2, y (0) = 1

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{64}{5}

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

4 y^{^{''}} + 4 y^{^{'}} + 325 y = 0, y (0) = 3, y^{^{'}} (0) = 2

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

What is the solution for y^{''}+5y^'-14y=0,y^'(0)=56 ?
The solution for y^{''}+5y^'-14y=0,y^'(0)=56 is y=(e^{2t}(56+7c_{2}))/2+c_{2}e^{-7t}