What is the solution for y^{''}+y^'+1/4 y=0 ?

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

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y^{''}+y^'+1/4 y=0

y^{^{''}} + y^{^{'}} + \frac{1}{4} y = 0

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

Solution steps

y^{''} (t) + y^{'} (t) + \frac{1}{4} y = 0

Solve linear ODE:

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

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

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\frac{d y}{d x} = y^{2} - 9

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