What is the solution for y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0 is y=e^{-8t}(cos(t)+8sin(t))

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y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 16 y^{^{'}} + 65 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = e^{- 8 t} (cos (t) + 8 sin (t))

Solution steps

y^{''} (t) + 16 y^{'} (t) + 65 y = 0

Solve linear ODE:

y = e^{- 8 t} (cos (t) + 8 sin (t))

y = e^{- 8 t} (cos (t) + 8 sin (t))

f (x) = 8 x^{\frac{1}{3}} - 5, at x = 8

3 y y^{^{'}} = x

\frac{d}{d t} (2^{t} - 2 t)

\frac{d}{d y} (x + 2 y)

\frac{s}{( s ^{2} + s + 1 )}

What is the solution for y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0 is y=e^{-8t}(cos(t)+8sin(t))