What is the solution for y^{''}+8y^'+17y=0,y(0)=0,y^'(0)=7 ?

The solution for y^{''}+8y^'+17y=0,y(0)=0,y^'(0)=7 is y=7e^{-4t}sin(t)

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y^{''}+8y^'+17y=0,y(0)=0,y^'(0)=7

y^{^{''}} + 8 y^{^{'}} + 17 y = 0, y (0) = 0, y^{^{'}} (0) = 7

y = 7 e^{- 4 t} sin (t)

Solution steps

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

Solve linear ODE:

y = 7 e^{- 4 t} sin (t)

y = 7 e^{- 4 t} sin (t)

(d^{3} - 5 d^{2} + 4 d - 20) x = 0

\frac{y ^{^{''}}}{y} = - a^{2}

9 y^{^{''}} - 5 y^{^{'}} = 0, y^{1} (0) = e^{- 7 x}

x^{^{''}} + 5 \cdot x = 0, x (1) = 0, x (0) = 0

(D^{4} - 1) y = 0

What is the solution for y^{''}+8y^'+17y=0,y(0)=0,y^'(0)=7 ?
The solution for y^{''}+8y^'+17y=0,y(0)=0,y^'(0)=7 is y=7e^{-4t}sin(t)