Pattern 1: Linear DE with IF (Most Frequent) JEE gives dy/dx + P(x)y = Q(x) with a specific IF. Common IFs: x^n, sec x, e^(x^2), (1+x^2). The solution form yIF = integral QIF dx + C is applied with an initial condition to find C.

Pattern 2: Homogeneous DE (High Frequency) Given dy/dx = (ax+by)/(cx+dy), recognize homogeneity and use y = vx. JEE often asks for the curve passing through a specific point.

Pattern 3: Formation of DE (Moderate) Given a 1- or 2-parameter family, find the DE. Key: count constants to determine order, then differentiate and eliminate.

Pattern 4: Bernoulli Equation (Moderate) dy/dx + Py = Qy^n typically with n=2 or n=-1. Recognize the y^n term on the right side.

Pattern 5: Exact Differentials (Moderate) Recognizing d(xy), d(y/x), d(arctan(y/x)) in disguised forms. JEE loves x dy - y dx expressions.

Pattern 6: Application Problems (Moderate) Growth/decay, cooling, or geometric properties (subnormal, subtangent). These translate to standard DE types.

Time-saving tips:

• Check separable first (quickest)
• For dy/dx = (linear in x,y)/(linear in x,y): check homogeneity, then try linear
• If y^n appears on RHS, it's Bernoulli
• x dy + y dx or x dy - y dx signals exact differential
• Always verify by substituting back if time permits