What is the solution for y^{''}+y^'+12y=0,y(0)=1 ?

The solution for y^{''}+y^'+12y=0,y(0)=1 is y=e^{-t/2}(cos((sqrt(47)t)/2)+c_{2}sin((sqrt(47)t)/2))

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y^{''}+y^'+12y=0,y(0)=1

y^{^{''}} + y^{^{'}} + 12 y = 0, y (0) = 1

y = e^{- \frac{t}{2}} (cos (\frac{47 t}{2}) + c_{2} sin (\frac{47 t}{2}))

Solution steps

y^{''} (t) + y^{'} (t) + 12 y = 0

Solve linear ODE:

y = e^{- \frac{t}{2}} (cos (\frac{47 t}{2}) + c_{2} sin (\frac{47 t}{2}))

y = e^{- \frac{t}{2}} (cos (\frac{47 t}{2}) + c_{2} sin (\frac{47 t}{2}))

What is the solution for y^{''}+y^'+12y=0,y(0)=1 ?
The solution for y^{''}+y^'+12y=0,y(0)=1 is y=e^{-t/2}(cos((sqrt(47)t)/2)+c_{2}sin((sqrt(47)t)/2))