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

The solution for y^{''}+y^'+y=0 is y=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))

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

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

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

Solution steps

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

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

\int (y^{5} + 5 y) d y

y^{^{''}} + y = 0, y (\frac{π}{3}) = 16, y^{^{'}} (\frac{π}{3}) = - 32

\frac{\partial}{\partial y} (7 e^{x^{2} l n (y)})

5 Y^{\frac{5}{8}} X^{\frac{3}{8}}

\int \frac{1}{3 x + 12} d x

What is the solution for y^{''}+y^'+y=0 ?
The solution for y^{''}+y^'+y=0 is y=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))