What is the solution for y^{''}-8y^'+16y=0,y(0)=2,y^'(0)=2 ?

The solution for y^{''}-8y^'+16y=0,y(0)=2,y^'(0)=2 is y=2e^{4t}-6e^{4t}t

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y^{''}-8y^'+16y=0,y(0)=2,y^'(0)=2

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 2

y = 2 e^{4 t} - 6 e^{4 t} t

Solution steps

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

Solve linear ODE:

y = 2 e^{4 t} - 6 e^{4 t} t

y = 2 e^{4 t} - 6 e^{4 t} t

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144 y^{^{'''}} + 120 y^{^{''}} + 25 y^{^{'}} = 0

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\frac{d ^{2}}{d x ^{2}} (\frac{3 x + 2}{2 x - 5})

What is the solution for y^{''}-8y^'+16y=0,y(0)=2,y^'(0)=2 ?
The solution for y^{''}-8y^'+16y=0,y(0)=2,y^'(0)=2 is y=2e^{4t}-6e^{4t}t