=0 ‌⇒xdy−3ydy+5dy+x‌dx+y‌dx+dx=0 ‌⇒(xdy+y‌dx)+5⋅dy−3ydy+x‌dx+dx=0 ‌⇒d(xy)+5dy−3ydy+x‌dx+dx=0 Now, integrating because every term is variable separable. xy+5y−‌
3y2
2
+‌
x2
2
+x=C Clearly, this equation is obtained by solving option 3(y−1)2−2(x+2)(y−1)−(x+2)2=C
