NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations
NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations, available at Myclass24, are designed to take students through one of the most conceptually rich chapters in the CBSE Class 12 curriculum. Differential equations connect rates of change to functional relationships, and solving them requires a combination of algebraic skill, integration techniques, and logical reasoning. Our solutions break down every problem type with clarity and precision.
Summary of Chapter 9 Differential Equations
Introduction: Order and degree of a differential equation, Examples, Formation of a differential equation. Methods of solving differential equations: variable separable. Homogeneous differential equation. Reducible to homogeneous differential equation, linear differential equation, Bernoulli’s equation, Inspection method, Orthogonal trajectory examples
Find the PDF of NCERT Solutions for Class 12 Maths Chapter 9
The PDF of NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations is available on Myclass24. Students can access all exercise-wise solutions in a clean, printable format. The PDF is structured to match the textbook order, making it easy to follow along while studying. Download and keep it handy during your revision sessions for quick reference before tests and board exams.
Detail | Information |
Chapter | Chapter 9 – Differential Equations |
Class | Class 12 Maths |
Board | CBSE (NCERT) |
Total Exercises | 6 Exercises + Miscellaneous |
Topics Covered | Order and Degree, Formation of DEs, Variable Separable, Homogeneous DEs, Linear DEs |
Difficulty Level | High |
Content By | Myclass24 |
About Chapter 9 – Differential Equations
Chapter 9 starts by establishing the language of differential equations — what order and degree mean, and how to identify them. Order refers to the highest derivative present in the equation, while degree is the power of that highest derivative after the equation has been made free of radicals and fractions. These definitions seem simple but need careful application when equations are written in unconventional forms.
Exercise 9.1 and 9.2 deal with determining order and degree, and Exercise 9.3 moves into forming differential equations from given general solutions. Here, students differentiate a general solution repeatedly, eliminating arbitrary constants to arrive at the differential equation it satisfies. This reverse process — going from solution to equation — is quite instructive because it builds an instinct for what certain DEs are likely to represent.
The variable separable method in Exercise 9.4 is the first solving technique introduced. The approach involves rearranging the equation so that all y-terms and dy are on one side and all x-terms and dx are on the other, then integrating both sides independently. It is elegant in its simplicity, but choosing the right manipulation requires practice.
Homogeneous differential equations, in Exercise 9.5, are a step up in complexity. These equations have the property that substituting y = vx reduces them to a separable form. The substitution step and the subsequent back-substitution of v = y/x need to be done carefully, and our solutions at Myclass24 handle both algebraic and trigonometric cases in detail.
Linear differential equations in Exercise 9.6 use the integrating factor method. Once students find the integrating factor — which is e raised to the integral of P(x) dx — multiplying both sides and using the product rule in reverse gives the solution in a standard form. This method has wide applications and is heavily tested in board exams.
At Myclass24, the Miscellaneous Exercise solutions include problems on application-based DEs such as growth and decay, Newton's law of cooling, and motion under gravity, making the chapter feel connected to the real world.
Why Study Chapter 9 from Myclass24?
At Myclass24, every solution for Chapter 9 is crafted keeping the CBSE exam pattern in mind. The explanations are written in plain language, the steps are numbered clearly, and important formulas are highlighted where needed. Students preparing for board exams, or anyone who wants to genuinely understand Differential Equations, will find Myclass24 solutions both reliable and thorough.