What is the solution for y^{''}+y^'+5/4 y=0 ?

The solution for y^{''}+y^'+5/4 y=0 is y=e^{-t/2}(c_{1}cos(t)+c_{2}sin(t))

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y^{''}+y^'+5/4 y=0

y^{^{''}} + y^{^{'}} + \frac{5}{4} y = 0

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

Solution steps

y^{''} (t) + y^{'} (t) + \frac{5}{4} y = 0

Solve linear ODE:

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

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

\frac{1}{8} x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = - 1, x^{^{'}} (0) = 14

4 y^{^{''}} + 24 y^{^{'}} + 37 y = 0

x^{^{''}} - 6 x^{^{'}} + 9 x = 0

y^{^{''}} + 144 y = 0

\frac{5}{8} x^{^{''}} + 40 x = 0

What is the solution for y^{''}+y^'+5/4 y=0 ?
The solution for y^{''}+y^'+5/4 y=0 is y=e^{-t/2}(c_{1}cos(t)+c_{2}sin(t))