Differential Equations for JEE Main 2026

Differential equations are a reliable calculus-based chapter that contributes one to two questions in JEE Main. The topic builds directly on integration, so a strong calculus foundation makes it far easier. Its problem types are well-defined and recurring, which means systematic practice converts directly into marks. This guide covers every method the 2026 exam will test, from the basics of order and degree to the solution of linear equations.

Basics: Order, Degree, and Formation

A differential equation relates a function to its derivatives, and the first skills are identifying its order, the highest derivative present, and its degree, the power of that highest derivative. These are quick conceptual questions that reward careful attention to the form of the equation. The formation of a differential equation from a general solution, by eliminating arbitrary constants through differentiation, is a standard reverse-direction question worth mastering. The number of arbitrary constants equals the order, a useful checking principle.

Be careful with degree: it is defined only when the equation is a polynomial in its derivatives, a subtlety that JEE tests in conceptual questions.

Variable Separable Equations

The simplest solvable type is the variable separable equation, where the variables can be rearranged onto opposite sides and each side integrated independently. This method is the foundation of the chapter, and many harder equations are reduced to this form. Master the technique and the integration skills it requires, since fluency with standard integrals directly determines your speed here. Equations reducible to variable separable form through a substitution are a common extension worth practicing. To test these, take a free mock test with a differential equations focus.

Because solving these equations is fundamentally an integration exercise, our calculus complete guide is essential background for this chapter.

Homogeneous Equations

A homogeneous differential equation is one where the right-hand side depends only on the ratio of the variables, and it is solved by a standard substitution that converts it into a variable separable form. Master recognizing a homogeneous equation and applying the substitution cleanly, because this is a reliable exam question type. Equations that are not homogeneous but can be made so through a shift of variables are a more advanced variation that occasionally appears.

The key skill is recognizing the homogeneous structure quickly, which lets you apply the standard substitution without hesitation.

Linear Differential Equations

The linear differential equation of the first order is the most important type for JEE, solved using an integrating factor. Master the standard form, the computation of the integrating factor, and the resulting solution, because this method is heavily tested and entirely mechanical once learned. Recognizing when an equation is linear, or can be made linear by treating the other variable as the dependent one, is a valuable skill that unlocks several harder problems.

Strategy for Differential Equations

The keys are identifying order and degree, recognizing the equation type, and applying the standard methods for variable separable, homogeneous, and linear equations fluently. Because the chapter rests on integration, master calculus first and study differential equations as its natural extension. Slot it into week one of your revision plan alongside calculus. Master the standard methods and this becomes a dependable, formulaic source of marks.