What is the solution for 25y^{''}+50y^'+169y=0,y(0)=4,y^'(0)=8 ?

The solution for 25y^{''}+50y^'+169y=0,y(0)=4,y^'(0)=8 is y=e^{-t}(4cos((12t)/5)+5sin((12t)/5))

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25y^{''}+50y^'+169y=0,y(0)=4,y^'(0)=8

25 y^{^{''}} + 50 y^{^{'}} + 169 y = 0, y (0) = 4, y^{^{'}} (0) = 8

y = e^{- t} (4 cos (\frac{12 t}{5}) + 5 sin (\frac{12 t}{5}))

Solution steps

25 y^{''} (t) + 50 y^{'} (t) + 169 y = 0

Solve linear ODE:

y = e^{- t} (4 cos (\frac{12 t}{5}) + 5 sin (\frac{12 t}{5}))

y = e^{- t} (4 cos (\frac{12 t}{5}) + 5 sin (\frac{12 t}{5}))

64 y^{^{''}} + 80 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} + \frac{0}{3} y^{^{'}} + \frac{12}{3} y = 0

3 y^{^{'''}} - 2 y^{^{''}} - 37 y^{^{'}} - 12 y = 0

- y^{^{''}} + 4 y^{^{'}} + 5 y = 0

What is the solution for 25y^{''}+50y^'+169y=0,y(0)=4,y^'(0)=8 ?
The solution for 25y^{''}+50y^'+169y=0,y(0)=4,y^'(0)=8 is y=e^{-t}(4cos((12t)/5)+5sin((12t)/5))