What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)= 82/5 ?

The solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)= 82/5 is y=4e^{4t}+(2e^{4t}t)/5

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y^{''}-8y^'+16y=0,y(0)=4,y^'(0)= 82/5

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = \frac{82}{5}

y = 4 e^{4 t} + \frac{2 e ^{4 t} t}{5}

Solution steps

y^{''} (t) - 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = 4 e^{4 t} + \frac{2 e ^{4 t} t}{5}

y = 4 e^{4 t} + \frac{2 e ^{4 t} t}{5}

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e^{x} y \frac{d y}{d x} = e^{- y} e^{- 2 x - y}

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What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)= 82/5 ?
The solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)= 82/5 is y=4e^{4t}+(2e^{4t}t)/5