Class 12 Mathematics Chapter 9 Differential Equations – Revision Notes

Differential Equations relates a function to its own derivatives, and this chapter shows three ways to solve them: separating variables, substituting y=vx for homogeneous forms, and using an integrating factor for linear ones.

Last Updated: September 23, 2026

Basics

• Order: highest derivative present. Degree: power of highest-order derivative.
• Formed by differentiating and eliminating arbitrary constants.

Solution Methods

• Variable separable: f(y)dy=g(x)dx, integrate both sides.
• Homogeneous: substitute y=vx.
• Linear dy/dx+Py=Q: IF=e^{∫P dx}, solution y·IF=∫Q·IF dx+C.

One-Line Summary

Differential equations relate a function to its derivatives; solved via variable separation, y=vx substitution for homogeneous forms, or integrating factors for linear forms.

Frequently Asked Questions

What is a differential equation, and what does solving one actually mean?
A differential equation is an equation involving a function and its derivatives; solving it means finding the original function that satisfies the given relationship between the function and its rates of change.

What is the difference between the order and degree of a differential equation?
The order is the highest derivative present in the equation, while the degree is the power of that highest-order derivative, once the equation is written as a polynomial in its derivatives.

Written by Satish

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