Rather than using the formal condition dM/dy = dN/dx, JEE problems are best solved by recognizing standard exact differential patterns. The key patterns: (1) x dy + y dx = d(xy) — appears whenever you see terms like xdy + ydx grouped together. (2) x dy - y dx = x^2d(y/x) — divide both sides by x^2 to get d(y/x). Equivalently = -y^2d(x/y). (3) (x dy - y dx)/(x^2 + y^2) = d(arctan(y/x)) — appears in polar-related DEs. (4) (x dx + y dy)/(x^2 + y^2) = d(ln(sqrt(x^2+y^2)))/1 — related to distance from origin. (5) e^x(f + f') dx = d(e^x*f(x)) — very common pattern in JEE. Recognizing these patterns can turn a seemingly complex DE into a one-step solution.