What is the solution for y^{''}-8y^'-9y=0,y(0)=0,y^'(0)=4 ?

The solution for y^{''}-8y^'-9y=0,y(0)=0,y^'(0)=4 is y= 2/5 e^{9t}-2/5 e^{-t}

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y^{''}-8y^'-9y=0,y(0)=0,y^'(0)=4

y^{^{''}} - 8 y^{^{'}} - 9 y = 0, y (0) = 0, y^{^{'}} (0) = 4

y = \frac{2}{5} e^{9 t} - \frac{2}{5} e^{- t}

Solution steps

y^{''} (t) - 8 y^{'} (t) - 9 y = 0

Solve linear ODE:

y = \frac{2}{5} e^{9 t} - \frac{2}{5} e^{- t}

y = \frac{2}{5} e^{9 t} - \frac{2}{5} e^{- t}

(D^{4} + 2 D^{3} + D^{2}) y = 0

y^{^{''}} + 2 y^{^{'}} - 5 y = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 1

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

y^{^{''}} + y = 0, y (\frac{π}{4}) = 0, y^{^{'}} (\frac{π}{4}) = - 3

What is the solution for y^{''}-8y^'-9y=0,y(0)=0,y^'(0)=4 ?
The solution for y^{''}-8y^'-9y=0,y(0)=0,y^'(0)=4 is y= 2/5 e^{9t}-2/5 e^{-t}