What is the solution for 36y^{''}+60y^'+25y=0 ?

The solution for 36y^{''}+60y^'+25y=0 is y=c_{1}e^{-(5t)/6}+c_{2}e^{-(5t)/6}t

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36y^{''}+60y^'+25y=0

36 y^{^{''}} + 60 y^{^{'}} + 25 y = 0

y = c_{1} e^{- \frac{5 t}{6}} + c_{2} e^{- \frac{5 t}{6}} t

Solution steps

36 y^{''} (t) + 60 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{5 t}{6}} + c_{2} e^{- \frac{5 t}{6}} t

y = c_{1} e^{- \frac{5 t}{6}} + c_{2} e^{- \frac{5 t}{6}} t

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What is the solution for 36y^{''}+60y^'+25y=0 ?
The solution for 36y^{''}+60y^'+25y=0 is y=c_{1}e^{-(5t)/6}+c_{2}e^{-(5t)/6}t