xdy/dx=uy

Question
Integrals
asked 2020-12-28
\(\displaystyle{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={u}{y}\)

Answers (1)

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.
0

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