What is the solution for y^{''}+y^'+y2=0 ?

The solution for y^{''}+y^'+y2=0 is y=e^{-t/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))

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y^{''}+y^'+y2=0

y^{^{''}} + y^{^{'}} + y 2 = 0

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

Solution steps

y^{''} (t) + y^{'} (t) + y 2 = 0

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y^{^{'''}} - 5 y^{^{''}} - 33 y^{^{'}} - 27 y = 0

- \frac{( y ^{^{''}} )}{( y ^{^{'}} )} = 4

49 y^{^{''}} - 70 y^{^{'}} + 25 y = 0

y^{^{''}} + (\frac{9.8}{1.5}) y = 0

y^{^{'''}} + 7 y^{^{''}} + 8 y^{^{'}} - 16 y = 0

What is the solution for y^{''}+y^'+y2=0 ?
The solution for y^{''}+y^'+y2=0 is y=e^{-t/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))