What is the solution for y^{''}+8y^'+65y=455,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+8y^'+65y=455,y(0)=0,y^'(0)=0 is y=e^{-4t}(-7cos(7t)-4sin(7t))+7

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y^{''}+8y^'+65y=455,y(0)=0,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 65 y = 455, y (0) = 0, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) + 8 y^{'} (t) + 65 y = 455

Solve linear ODE:

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

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

\int \frac{1}{x ^{2} + 6 x + 18} d x

x \to 1 lim (x - 4)

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\frac{d}{d x} ((x^{3} - 8)^{\frac{2}{3}})

x \to 3 - lim (x^{2} - 8)

What is the solution for y^{''}+8y^'+65y=455,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+8y^'+65y=455,y(0)=0,y^'(0)=0 is y=e^{-4t}(-7cos(7t)-4sin(7t))+7