What is the solution for (dx)/(dt)=x^2e^{-2t},x(0)=3 ?

The solution for (dx)/(dt)=x^2e^{-2t},x(0)=3 is x=-(6e^{2t})/(-3+e^{2t)}

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(dx)/(dt)=x^2e^{-2t},x(0)=3

\frac{d x}{d t} = x^{2} e^{- 2 t}, x (0) = 3

x = - \frac{6 e ^{2 t}}{- 3 + e ^{2 t}}

Solution steps

\frac{d x}{d t} = x^{2} e^{- 2 t}

Solve separable ODE:

x = - \frac{6 e ^{2 t}}{- 3 + e ^{2 t}}

x = - \frac{6 e ^{2 t}}{- 3 + e ^{2 t}}

f (x) = \frac{1}{9 x}, at x = 9

\int cos (\frac{π}{x}) d x

f (x) = x (2 x + 2)

x \to 1 lim (\frac{5 - x ^{2}}{1 + x})

\int 0.1

What is the solution for (dx)/(dt)=x^2e^{-2t},x(0)=3 ?
The solution for (dx)/(dt)=x^2e^{-2t},x(0)=3 is x=-(6e^{2t})/(-3+e^{2t)}