Use $\displaystyle y = u^k$ to prove

$\displaystyle \frac{dy}{dx}= y - (y^4)x$

can be rewritten as

$\displaystyle

\frac{d}{dx} (e^{3x}u) = 3xe^{3x}

$

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- Aug 30th 2009, 12:10 PMPaul616Substituting into a differential equation
Use $\displaystyle y = u^k$ to prove

$\displaystyle \frac{dy}{dx}= y - (y^4)x$

can be rewritten as

$\displaystyle

\frac{d}{dx} (e^{3x}u) = 3xe^{3x}

$ - Aug 30th 2009, 12:13 PMMatt Westwood
Standard Bernoulii diffeq: set $\displaystyle u - y^{-3}$ and see what happens.