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Differential Equations

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A Simple Example of a Separable Equation

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The equation:

$$\begin{equation} \frac{dy}{dx} = \frac{x^3}{1+y^3} \end{equation}$$

...is separable. The integral curves satisfy:

A

$y + y^4 - x^4 = \textrm{constant}$

B

$y + \cfrac{y^4}{4} - \cfrac{x^4}{4} = 0$

C

$y + \cfrac{y^4}{4} + \cfrac{x^4}{4} = \textrm{constant}$

D

$y + \cfrac{y^4}{4} - \cfrac{x^4}{4} = \textrm{constant}$