What is the solution for (d^2x)/(dt^2)-4(dx)/(dt)+4x=2t ?

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

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(d^2x)/(dt^2)-4(dx)/(dt)+4x=2t

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

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{t}{2} + \frac{1}{2}

Solution steps

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

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{t}{2} + \frac{1}{2}

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{t}{2} + \frac{1}{2}

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