What is the solution for y^{''}+y^'+(pi^2+1/4)y=0 ?

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

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y^{''}+y^'+(pi^2+1/4)y=0

y^{^{''}} + y^{^{'}} + (π^{2} + \frac{1}{4}) y = 0

y = e^{- \frac{t}{2}} (c_{1} cos (π t) + c_{2} sin (π t))

Solution steps

y^{''} (t) + y^{'} (t) + (π^{2} + \frac{1}{4}) y = 0

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (π t) + c_{2} sin (π t))

y = e^{- \frac{t}{2}} (c_{1} cos (π t) + c_{2} sin (π t))

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