What is the solution for y^{''}-6y^'+8y=0,y(0)=0,y^'(0)=-2 ?

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

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y^{''}-6y^'+8y=0,y(0)=0,y^'(0)=-2

y^{^{''}} - 6 y^{^{'}} + 8 y = 0, y (0) = 0, y^{^{'}} (0) = - 2

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

y^{^{'''}} + k y = 0

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

y^{^{''}} + 2 y^{^{'}} = 0, y (0) = - 28, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 7 y = 0

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