What is the solution for y^{''}+4y^'-5y=0,y(0)=2,y^'(0)=14 ?

The solution for y^{''}+4y^'-5y=0,y(0)=2,y^'(0)=14 is y=4e^t-2e^{-5t}

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y^{''}+4y^'-5y=0,y(0)=2,y^'(0)=14

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 14

y = 4 e^{t} - 2 e^{- 5 t}

Solution steps

y^{''} (t) + 4 y^{'} (t) - 5 y = 0

Solve linear ODE:

y = 4 e^{t} - 2 e^{- 5 t}

y = 4 e^{t} - 2 e^{- 5 t}

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x^{^{''}} - (\frac{π}{2})^{2} x = 0

What is the solution for y^{''}+4y^'-5y=0,y(0)=2,y^'(0)=14 ?
The solution for y^{''}+4y^'-5y=0,y(0)=2,y^'(0)=14 is y=4e^t-2e^{-5t}