What is the solution for 64y^{''}+80y^'+16y=0,y(0)=0,y^'(0)=1 ?

The solution for 64y^{''}+80y^'+16y=0,y(0)=0,y^'(0)=1 is y= 4/3 e^{-t/4}-4/3 e^{-t}

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

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

y = \frac{4}{3} e^{- \frac{t}{4}} - \frac{4}{3} e^{- t}

Solution steps

64 y^{''} (t) + 80 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = \frac{4}{3} e^{- \frac{t}{4}} - \frac{4}{3} e^{- t}

y = \frac{4}{3} e^{- \frac{t}{4}} - \frac{4}{3} e^{- t}

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

4 y^{^{''}} - 12 y^{^{'}} + 9 y = 0, y (0) = 1

What is the solution for 64y^{''}+80y^'+16y=0,y(0)=0,y^'(0)=1 ?
The solution for 64y^{''}+80y^'+16y=0,y(0)=0,y^'(0)=1 is y= 4/3 e^{-t/4}-4/3 e^{-t}