What is the solution for y^{''}+12y^'+37y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+12y^'+37y=0,y(0)=1,y^'(0)=0 is y=e^{-6t}(cos(t)+6sin(t))

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y^{''}+12y^'+37y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 12 y^{^{'}} + 37 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) + 12 y^{'} (t) + 37 y = 0

Solve linear ODE:

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

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

\int_{0}^{1} \frac{23}{4 y - 1} d y

f (x) = cos^{3} (π x)

\int \frac{x ^{2} - 400}{x} d x

\int \frac{0}{x + 1} d x

x \to 0 lim (e^{2 x})

What is the solution for y^{''}+12y^'+37y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+12y^'+37y=0,y(0)=1,y^'(0)=0 is y=e^{-6t}(cos(t)+6sin(t))