[tex]xy'=\sqrt{x^2-y^2}+y\\\\x\frac{dy}{dx}=\sqrt{x^2-y^2}+y \:\:\: /:x\:\:(x\neq 0)\\\\\frac{dy}{dx}=\sqrt{\frac{x^2-y^2}{x^2}}+\frac{y}{x}\\\\\frac{dy}{dx}=\sqrt{1-\frac{y^2}{x^2}}+\frac{y}{x}\\\\\\ podstawienie:\\u = \frac{y}{x}\\y =xu \:\: /() \frac{d}{dx}\\ \frac{dy}{dx}=u+x\frac{du}{dx}\\\\\\u+x\frac{du}{dx}=\sqrt{1-u^2}+u \; \\\\x\frac{du}{dx}=\sqrt{1-u^2}\\\\ \frac{du}{\sqrt{1-u^2}}=\frac{dx}{x}\:\: /\int \\\\ arcsinu=ln|x|+C\\\\u=sin(ln|x|+C)\\\\y=xsin(ln|x|+C)[/tex]
(-_-(-_-)-_-)
