What is the solution for y^{''}-4y^'-5y=0,y(-1)=3,y(-1)=9 ?

The solution for y^{''}-4y^'-5y=0,y(-1)=3,y(-1)=9 is y=(3e^5-e^6c_{2})e^{5t}+c_{2}e^{-t}

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y^{''}-4y^'-5y=0,y(-1)=3,y(-1)=9

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y (- 1) = 9

y = (3 e^{5} - e^{6} c_{2}) e^{5 t} + c_{2} e^{- t}

Solution steps

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

Solve linear ODE:

y = (3 e^{5} - e^{6} c_{2}) e^{5 t} + c_{2} e^{- t}

y = (3 e^{5} - e^{6} c_{2}) e^{5 t} + c_{2} e^{- t}

What is the solution for y^{''}-4y^'-5y=0,y(-1)=3,y(-1)=9 ?
The solution for y^{''}-4y^'-5y=0,y(-1)=3,y(-1)=9 is y=(3e^5-e^6c_{2})e^{5t}+c_{2}e^{-t}