# xdy/dx=uy

Question
Integrals
$$\displaystyle{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={u}{y}$$

2020-12-29
Given that $$\displaystyle{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}{y}$$
$$\displaystyle\to\frac{{\left.{d}{y}\right.}}{{y}}={4}{\left(\frac{{\left.{d}{x}\right.}}{{x}}\right)}$$
$$\displaystyle\to∫\frac{{\left.{d}{y}\right.}}{{x}}={4}∫{\left(\frac{{\left.{d}{x}\right.}}{{x}}\right)}+{\ln{{e}}}$$
$$\displaystyle\to{\ln{{y}}}={4}{\ln{{x}}}+{\ln{{c}}}$$
PSK->y=ex^4
where c is a arbitrary constant.

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