What is the solution for y^{''}+8y^'+17y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+8y^'+17y=0,y(0)=1,y^'(0)=0 is y=e^{-4t}(cos(t)+4sin(t))

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y^{''}+8y^'+17y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 17 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = e^{- 4 t} (cos (t) + 4 sin (t))

Solution steps

y^{''} (t) + 8 y^{'} (t) + 17 y = 0

Solve linear ODE:

y = e^{- 4 t} (cos (t) + 4 sin (t))

y = e^{- 4 t} (cos (t) + 4 sin (t))

\int \frac{( x + 2 ) ^{8}}{2 x} d x

e^{- 5}

\int 3 e^{- 0.1 x} d x

x^{2} y d x + y (x^{3} + e^{3 y}) d y = 0

x \to 2 lim (\frac{( 7 x ^{5} - 10 x ^{4} - 13 x + 6 )}{( 3 x ^{2} - 6 x - 8 )})

What is the solution for y^{''}+8y^'+17y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+8y^'+17y=0,y(0)=1,y^'(0)=0 is y=e^{-4t}(cos(t)+4sin(t))