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

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

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

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

y = - 4 e^{4 t} + 16 e^{4 t} t

Solution steps

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

Solve linear ODE:

y = - 4 e^{4 t} + 16 e^{4 t} t

y = - 4 e^{4 t} + 16 e^{4 t} t

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