What is the solution for y^{''}-5y^'-36y=0,y(0)=-2,y^'(0)=3 ?

The solution for y^{''}-5y^'-36y=0,y(0)=-2,y^'(0)=3 is y=(-2+21/13)e^{9t}-21/13 e^{-4t}

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y^{''}-5y^'-36y=0,y(0)=-2,y^'(0)=3

y^{^{''}} - 5 y^{^{'}} - 36 y = 0, y (0) = - 2, y^{^{'}} (0) = 3

y = (- 2 + \frac{21}{13}) e^{9 t} - \frac{21}{13} e^{- 4 t}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 36 y = 0

Solve linear ODE:

y = (- 2 + \frac{21}{13}) e^{9 t} - \frac{21}{13} e^{- 4 t}

y = (- 2 + \frac{21}{13}) e^{9 t} - \frac{21}{13} e^{- 4 t}

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 5, y^{^{'}} (0) = 33

y^{^{''}} - 16 y = 0, y (0) = 3

2 y^{^{''}} - 5 y^{^{'}} - 3 y = 3 y

10000 y^{^{''}} - 81 y^{^{'}} = 0, y (0) = 8, y^{^{'}} (0) = 5

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 8, y (1) = 0

What is the solution for y^{''}-5y^'-36y=0,y(0)=-2,y^'(0)=3 ?
The solution for y^{''}-5y^'-36y=0,y(0)=-2,y^'(0)=3 is y=(-2+21/13)e^{9t}-21/13 e^{-4t}