What is the solution for y^{''}+2y+1=0 ?

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

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y^{''}+2y+1=0

y^{^{''}} + 2 y + 1 = 0

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

Solution steps

y^{''} (t) + 2 y + 1 = 0

Solve linear ODE:

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

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

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