What is the solution for y^{''}+5y^'+6.25y=0 ?

The solution for y^{''}+5y^'+6.25y=0 is y=c_{1}e^{-(5t)/2}+c_{2}e^{-(5t)/2}t

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y^{''}+5y^'+6.25y=0

y^{^{''}} + 5 y^{^{'}} + 6.25 y = 0

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

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6.25 y = 0

Solve linear ODE:

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

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

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\frac{1}{s + 40}

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What is the solution for y^{''}+5y^'+6.25y=0 ?
The solution for y^{''}+5y^'+6.25y=0 is y=c_{1}e^{-(5t)/2}+c_{2}e^{-(5t)/2}t