Lösen Sie die DGL ((xy)/(x^2-x))*y´=pi-1

Question

sen Sie die DGL ((xy)/(x^2-x))*y´=pi-1

Answer 1

$$ \frac{xy}{x^2-x}y'=\pi-1\\ yy'=\frac{(\pi-1)(x^2-x)}{x}\\y\frac{dy}{dx}=\frac{(\pi-1)(x^2-x)}{x}\\ \int ydy=\int \frac{(\pi-1)(x^2-x)}{x}dx\\\frac{1}{2}y^2=(\pi-1)\int (x-1)dx\\\frac{1}{2}y^2=(\pi-1)\left(\frac{1}{2}x^2-x\right)+C\\y^2=(\pi-1)\left(x^2-2x\right)+2C\\y=\pm\sqrt{(\pi-1)(x^2-2x)+2C}$$

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