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Question Number 174367 by Mastermind last updated on 30/Jul/22

$$\mathrm{solve}$$$${\mathrm{y}}^{10}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)+\frac{{\mathrm{y}}^{11}}{(\mathrm{x}-1)}={\mathrm{xy}}^{12}$$

Commented by infinityaction last updated on 31/Jul/22

$$\frac{1}{y^2}\left(\frac{dy}{dx}\right)+\frac{1}{y}\cdot \frac{1}{(x-1)}=x$$$$let\frac{1}{y}=v$$$$\frac{1}{y^2}\left(\frac{dy}{dx}\right)=-\frac{dv}{dx}$$$$-\frac{dv}{dx}+\frac{1}{y}\cdot \frac{1}{(x-1)}=x$$$$\frac{dv}{dx}+\frac{1}{y}\cdot \frac{1}{(1-x)}=-x$$

Commented by peter frank last updated on 01/Aug/22

$$\mathrm{thanks}$$

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