What is the solution for y^{''}+2y^'+37y=0,y(0)=-3,y^'(0)=21 ?

The solution for y^{''}+2y^'+37y=0,y(0)=-3,y^'(0)=21 is y=e^{-t}(-3cos(6t)+3sin(6t))

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y^{''}+2y^'+37y=0,y(0)=-3,y^'(0)=21

y^{^{''}} + 2 y^{^{'}} + 37 y = 0, y (0) = - 3, y^{^{'}} (0) = 21

y = e^{- t} (- 3 cos (6 t) + 3 sin (6 t))

Solution steps

y^{''} (t) + 2 y^{'} (t) + 37 y = 0

Solve linear ODE:

y = e^{- t} (- 3 cos (6 t) + 3 sin (6 t))

y = e^{- t} (- 3 cos (6 t) + 3 sin (6 t))

\frac{d}{d y} ((2 - y^{2} + x^{2}) e^{(1 - x^{2} - \frac{y ^{2}}{4})})

\frac{d}{d x} (36 e^{- 2 x})

f (x) = - 3 e^{4 x}

\int - 4 x^{- 5} d x

\int \frac{1}{( x ^{2} )} d x

What is the solution for y^{''}+2y^'+37y=0,y(0)=-3,y^'(0)=21 ?
The solution for y^{''}+2y^'+37y=0,y(0)=-3,y^'(0)=21 is y=e^{-t}(-3cos(6t)+3sin(6t))