What is the solution for 10y^{''}+60y^'+50y=0 ?

The solution for 10y^{''}+60y^'+50y=0 is y=c_{1}e^{-t}+c_{2}e^{-5t}

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10y^{''}+60y^'+50y=0

10 y^{^{''}} + 60 y^{^{'}} + 50 y = 0

y = c_{1} e^{- t} + c_{2} e^{- 5 t}

Solution steps

10 y^{''} (t) + 60 y^{'} (t) + 50 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 5 t}

y = c_{1} e^{- t} + c_{2} e^{- 5 t}

\frac{d}{d x} (e^{\frac{- x}{3}})

\int e^{2 θ} cos (3 θ) d θ

y = 2 x^{2} - 12 x + 6

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

\frac{d}{d x} (π \cdot x^{2})

What is the solution for 10y^{''}+60y^'+50y=0 ?
The solution for 10y^{''}+60y^'+50y=0 is y=c_{1}e^{-t}+c_{2}e^{-5t}