If xdy=ydx+y2dy,y>0 andy(1)=1, then what is y(−3) equal to?

[a] Given, xdy=ydx+y2dy$\Rightarrow 1=4xdxdy+y2x\Rightarrow dxdy+y=xy$⇒dxdy=xy=−y                          ? (1)$P=-1y,Q=-y$IF =e∫Pdy=e∫e−1ydy=e−logy=1y$M\underline{t}iply\in gEqn.\left(1\right)byIF$⇒1ydxdy−xy2=−1; xy=∫1y(−y)dy+C$\Rightarrow xy=\int -1dy+C\Rightarrow xy=-y+C$y(1)=1$11=-1+C\Rightarrow C=2$⇒xy=−y+2⇒x=−y2+2y$\Rightarrow y\left(-3\right)\Rightarrow -3=-y2+2y\Rightarrow y2-2y-3=0$⇒y=+2±4+12−−−−−√2=2±42⇒y=3,−1\displaystyle{\Sin{{c}}}{e}{y}>{0}{s}{o}{y}={3}.