What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=10 ?

The solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=10 is y=4e^{4t}-6e^{4t}t

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y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=10

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 10

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

Solution steps

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

Solve linear ODE:

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

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

\frac{1}{y} y^{^{''}} = a, y (0) = 0

y^{^{''''}} - 3 y^{^{''}} + 2 y = 0

y^{^{''}} - y = 0, y (0) = 0, y^{^{'}} (0) = 7

y^{^{''}} - y = 0, y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + 12 y^{^{'}} + 8 y = 0

What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=10 ?
The solution for y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=10 is y=4e^{4t}-6e^{4t}t