What is the solution for y^{''}+5y^'-24y=0 ?

The solution for y^{''}+5y^'-24y=0 is y=c_{1}e^{3t}+c_{2}e^{-8t}

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y^{''}+5y^'-24y=0

y^{^{''}} + 5 y^{^{'}} - 24 y = 0

y = c_{1} e^{3 t} + c_{2} e^{- 8 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) - 24 y = 0

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 8 t}

y = c_{1} e^{3 t} + c_{2} e^{- 8 t}

\int \frac{3 x - 1}{x ^{2} - 3 x - 4} d x

\int e^{2 t + e^{t}} d t

\frac{d}{d x} ((5 x^{2} - 2 x + 1)^{- 3})

x \to 3 lim (\frac{2 + x}{x - 3})

\frac{d}{d t} (2 t^{2} - 10)

What is the solution for y^{''}+5y^'-24y=0 ?
The solution for y^{''}+5y^'-24y=0 is y=c_{1}e^{3t}+c_{2}e^{-8t}