What is the solution for y^{''}-5y^'-14y=0,y(0)=0,y^'(0)=3 ?

The solution for y^{''}-5y^'-14y=0,y(0)=0,y^'(0)=3 is y= 1/3 e^{7t}-1/3 e^{-2t}

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y^{''}-5y^'-14y=0,y(0)=0,y^'(0)=3

y^{^{''}} - 5 y^{^{'}} - 14 y = 0, y (0) = 0, y^{^{'}} (0) = 3

y = \frac{1}{3} e^{7 t} - \frac{1}{3} e^{- 2 t}

Solution steps

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

Solve linear ODE:

y = \frac{1}{3} e^{7 t} - \frac{1}{3} e^{- 2 t}

y = \frac{1}{3} e^{7 t} - \frac{1}{3} e^{- 2 t}

4 y^{^{''}} - 4 y^{^{'}} + (- 3) y = 0, y (0) = 5, y^{^{'}} (0) = 0

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

y^{^{''}} + 0.25 y = 0

\frac{17}{160} y^{^{''}} + \frac{4}{10} y^{^{'}} + 2 y = 0

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

What is the solution for y^{''}-5y^'-14y=0,y(0)=0,y^'(0)=3 ?
The solution for y^{''}-5y^'-14y=0,y(0)=0,y^'(0)=3 is y= 1/3 e^{7t}-1/3 e^{-2t}