What is the solution for 4(y^{''})+4(y^')+y=0 ?

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

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4(y^{''})+4(y^')+y=0

4 (y^{^{''}}) + 4 (y^{^{'}}) + y = 0

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

Solution steps

4 (y^{''} (t)) + 4 (y^{'} (t)) + 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

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