What is the solution for (d^2y)/(dt^2)-4(dy)/(dt)+4y=0 ?

The solution for (d^2y)/(dt^2)-4(dy)/(dt)+4y=0 is y=c_{1}e^{2t}+c_{2}te^{2t}

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(d^2y)/(dt^2)-4(dy)/(dt)+4y=0

\frac{d ^{2} y}{d t ^{2}} - 4 \frac{d y}{d t} + 4 y = 0

y = c_{1} e^{2 t} + c_{2} t e^{2 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 4 \frac{d y}{d t} + 4 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t}

y = c_{1} e^{2 t} + c_{2} t e^{2 t}

y^{^{'''}} + 7 y^{^{''}} - 10 y = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y^{^{'}} (0) = - 2

y^{^{''''}} + 3 y^{^{'''}} - 4 y^{^{''}} = 0

y^{^{''}} - 7 y^{^{'}} + 3 y = 0

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

What is the solution for (d^2y)/(dt^2)-4(dy)/(dt)+4y=0 ?
The solution for (d^2y)/(dt^2)-4(dy)/(dt)+4y=0 is y=c_{1}e^{2t}+c_{2}te^{2t}