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Differential Equations

NCERT Class 12 Mathematics Chapter 9

Differential Equations for Class 12 Maths and JEE: order and degree, general and particular solutions, separable, homogeneous and linear equations.

3 topics Updated 8 Nov 2026

For: Class 12 and JEE

In the syllabus: JEE Class 12 syllabus

With your textbook

NCERT Mathematics Part II (Class 12), Chapter 9 “Differential Equations”, reprint 2026-27.

Open the official NCERT chapter (PDF, 3.4 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Order and degree of a differential equation

    Order and degree of differential equations for Class 12 Maths and JEE: the highest derivative, when the degree is not defined, all of NCERT Exercise 9.1.

    NCERT Section 9.2 10 min read 5 solved examples 10 practice questions

  2. General and particular solutions of a differential equation

    General and particular solutions for Class 12 Maths and JEE: checking a solution by substitution, counting arbitrary constants, all of NCERT Exercise 9.2.

    NCERT Section 9.3 11 min read 5 solved examples 10 practice questions

  3. Solving first order, first degree differential equations

    Variable separable, homogeneous and linear differential equations for Class 12 Maths and JEE: y = vx, the integrating factor, linear in x, solved examples.

    NCERT Section 9.4 19 min read 7 solved examples 13 practice questions

Key formulas in this chapter

Order and degree

  • order = order of the highest derivative
  • degree = highest power of the highest order derivative
  • degree not defined if a derivative stays inside sin, cos, log or exp

General and particular solutions

  • solution: substitute y and its derivatives; L.H.S. = R.H.S.
  • general solution of order n: n arbitrary constants
  • particular solution: no arbitrary constants

Solving first order equations

  • dy/h(y) = g(x) dx for h(y) ≠ 0; check constant solutions h(y) = 0
  • homogeneous: y = vx, dy/dx = v + x dv/dx
  • linear: I.F. = e to the power ∫P dx; y × I.F. = ∫(Q × I.F.) dx + C
  • linear in x: I.F. = e to the power ∫P dy; x × I.F. = ∫(Q × I.F.) dy + C

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