What is the solution for y^{''}+6y^'+11y=0 ?

The solution for y^{''}+6y^'+11y=0 is y=e^{-3t}(c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t))

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y^{''}+6y^'+11y=0

y^{^{''}} + 6 y^{^{'}} + 11 y = 0

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 11 y = 0

Solve linear ODE:

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

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

\int (2 - cos (x))^{2} d x

\frac{d y}{d x}, 7 x y + 6 = 0

\int \frac{x ^{2}}{x ^{3} + 8} d x

x \to 1 lim (\frac{x + 3}{x - 1})

\int 12 x d x

What is the solution for y^{''}+6y^'+11y=0 ?
The solution for y^{''}+6y^'+11y=0 is y=e^{-3t}(c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t))