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

The solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=4 is y=4e^{4t}-12e^{4t}t

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

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

y = 4 e^{4 t} - 12 e^{4 t} t

Solution steps

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

Solve linear ODE:

y = 4 e^{4 t} - 12 e^{4 t} t

y = 4 e^{4 t} - 12 e^{4 t} t

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 12, y^{^{'}} (0) = - 52

y^{^{''}} + y = 0, y (0) = 13, y (0) = 29

3 (\frac{d ^{2} y}{d x ^{2}}) + 19 (\frac{d y}{d x}) - 14 y = 0

6 y^{^{'''}} + 2 y^{^{''}} = 0

(d^{3} + 8) y = 0

What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=4 ?
The solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=4 is y=4e^{4t}-12e^{4t}t