What is the solution for y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11 ?

The solution for y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11 is y=3e^{4t}-e^{4t}t

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y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 11

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

Solution steps

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

Solve linear ODE:

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

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

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What is the solution for y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11 ?
The solution for y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11 is y=3e^{4t}-e^{4t}t