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# 找出可分离方程

$\begin{array}{rl}\frac{dy}{dx}& =\stackrel{f\left(y\right)}{\stackrel{⏞}{\mathrm{sin}\left(y\right)}}\stackrel{g\left(x\right)}{\stackrel{⏞}{\mathrm{ln}\left(x\right)}}\\ \\ \frac{1}{\mathrm{sin}\left(y\right)}dy& =\mathrm{ln}\left(x\right)\phantom{\rule{0.167em}{0ex}}dx\\ \end{array}$
$\begin{array}{rl}\frac{dy}{dx}& =\frac{\stackrel{g\left(x\right)}{\stackrel{⏞}{{x}^{3}-5x}}}{\underset{f\left(y\right)}{\underset{⏟}{{e}^{y}}}}\\ \\ {e}^{y}\phantom{\rule{0.167em}{0ex}}dy& =\left({x}^{3}-5x\right)\phantom{\rule{0.167em}{0ex}}dx\\ \end{array}$
$\begin{array}{rl}\frac{dy}{dx}& =\frac{\stackrel{f\left(y\right)}{\stackrel{⏞}{\sqrt{y}}}}{\underset{g\left(x\right)}{\underset{⏟}{\mathrm{cos}\left(x\right)}}}\\ \\ \frac{1}{\sqrt{y}}dy& =\frac{1}{\mathrm{cos}\left(x\right)}dx\end{array}$

$\frac{dy}{dx}=xy-7x=\stackrel{g\left(x\right)}{\stackrel{⏞}{x}}\stackrel{f\left(y\right)}{\stackrel{⏞}{\left(y-7\right)}}$

$\frac{dy}{dx}=3y-{x}^{2}y$

$\frac{dy}{dx}=4x+5y+4$

$\frac{dy}{dx}={2}^{y-x}$