Differential Equations Class 12 Notes for IIT JEE

The variable separable method is the most straightforward — separate x and y terms on opposite sides, then integrate both. However, the linear differential equation method (integrating factor) is more frequently tested in JEE Main. Mastering both methods and knowing when to apply each one is the fastest route to scoring full marks on this topic.

Based on NTA's official JEE Main papers from 2020 to 2026, differential equations feature in 1 to 2 questions per session, contributing 4 to 8 marks. The topic appears in almost every session, making it one of the more reliable scoring areas in Class 12 Mathematics.

Order is the highest derivative present in the equation. Degree is the power to which that highest derivative is raised, after the equation is written as a polynomial in its derivatives. If a transcendental function (like sin or log) is applied to a derivative, the degree is undefined. Order is always defined for a valid differential equation.

Yes. JEE Advanced tests differential equations at a higher conceptual level — often linking them with coordinate geometry (tangent/normal problems), integration techniques, and exact differentials. Problems may require reducing a non-standard ODE to a recognisable form. Students aiming for IITs should practise beyond NCERT and work through past JEE Advanced papers.

For a homogeneous differential equation dy/dx = f(y/x), substitute y = vx, which gives dy/dx = v + x·dv/dx. This converts the equation into a variable separable form in v and x, which can then be integrated directly. After integrating, back-substitute v = y/x to get the solution in terms of x and y.