What is the solution for y^{''}+5y^'-36y=0 ?

The solution for y^{''}+5y^'-36y=0 is y=c_{1}e^{4t}+c_{2}e^{-9t}

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y^{''}+5y^'-36y=0

y^{^{''}} + 5 y^{^{'}} - 36 y = 0

y = c_{1} e^{4 t} + c_{2} e^{- 9 t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 9 t}

y = c_{1} e^{4 t} + c_{2} e^{- 9 t}

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 0

3 y^{^{''}} + 8 y^{^{'}} - 3 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

\int 5 sec (x) d x

\frac{\partial}{\partial x} (25 - x^{2} - y^{2})

\int_{0}^{\infty} y e^{- y} d y

What is the solution for y^{''}+5y^'-36y=0 ?
The solution for y^{''}+5y^'-36y=0 is y=c_{1}e^{4t}+c_{2}e^{-9t}