Question Number 165503 by metamorfose last updated on 02/Feb/22
$${y}'\left({x}\right)=\frac{{xln}\left({y}\left({x}\right)\right)}{{ln}\left({x}\right){y}\left({x}\right)}\:,\:{y}\left({x}\right)=???. \\ $$
Answered by TheSupreme last updated on 02/Feb/22
$$\frac{{yy}'}{{ln}\left({y}\right)}=\frac{{x}}{{ln}\left({x}\right)} \\ $$$$\frac{{x}}{{ln}\left({x}\right)}=\frac{{y}\:\frac{{dy}}{{dx}}}{{ln}\left({y}\right)} \\ $$$$\frac{{xdx}}{{ln}\left({x}\right)}=\frac{{ydy}}{{ln}\left({y}\right)} \\ $$$$ \\ $$$${f}\left({x}\right){dx}={f}\left({y}\left({x}\right)\right){dy}\:\forall{x}\:\rightarrow{y}\left({x}\right)={x}\: \\ $$$$ \\ $$
Commented by metamorfose last updated on 04/Feb/22
$${thnx}\:{sir}\:{but}\:{this}\:{is}\:{not}\:{a}\:{general}\:{solution}\: \\ $$$$ \\ $$