What is the solution for 25y^{''}+80y^'+64y=0,y(0)=8 ?

The solution for 25y^{''}+80y^'+64y=0,y(0)=8 is y=8e^{-(8t)/5}+c_{2}e^{-(8t)/5}t

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25y^{''}+80y^'+64y=0,y(0)=8

25 y^{^{''}} + 80 y^{^{'}} + 64 y = 0, y (0) = 8

y = 8 e^{- \frac{8 t}{5}} + c_{2} e^{- \frac{8 t}{5}} t

Solution steps

25 y^{''} (t) + 80 y^{'} (t) + 64 y = 0

Solve linear ODE:

y = 8 e^{- \frac{8 t}{5}} + c_{2} e^{- \frac{8 t}{5}} t

y = 8 e^{- \frac{8 t}{5}} + c_{2} e^{- \frac{8 t}{5}} t

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 9, y^{^{'}} (0) = 5

7 y^{^{''}} - 8 y^{^{'}} + y = 0, y (0) = 7, y^{^{'}} (0) = \frac{1}{7}

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = \frac{3}{5}, y^{^{'}} (0) = \frac{1}{5}

y^{^{''}} + 16 y = 0, y (0) = sin (k t)

2 y^{^{''}} = 3 y

What is the solution for 25y^{''}+80y^'+64y=0,y(0)=8 ?
The solution for 25y^{''}+80y^'+64y=0,y(0)=8 is y=8e^{-(8t)/5}+c_{2}e^{-(8t)/5}t