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.
NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations FAQs
A differential equation is an equation that contains a function along with one or more of its derivatives. It describes the relationship between a variable and its rate of change. In Chapter 9, students learn how differential equations are formed and solved using various methods. These equations are widely used in mathematics, physics, engineering, economics, and many other fields to model real-life situations. NCERT exercises introduce the basic concepts and provide step-by-step problems to strengthen understanding. Learning differential equations is important because it helps students apply calculus concepts to practical situations and prepares them for advanced studies in mathematics.
Determining the order and degree is one of the most frequently asked topics in this chapter. The order of a differential equation is the highest-order derivative present in the equation. The degree refers to the power of the highest-order derivative after the equation has been expressed in polynomial form with respect to derivatives. Students often confuse these two terms, leading to incorrect answers. NCERT exercises include several examples that help clarify the distinction. Understanding order and degree is essential because many solution methods depend on correctly identifying these characteristics before attempting to solve the equation.
Formation of differential equations involves eliminating arbitrary constants from a given family of curves. Students first differentiate the equation as many times as necessary and then remove the constants to obtain a differential equation. NCERT exercises contain several problems where students are required to form equations from algebraic and geometric relationships. This topic helps students understand how differential equations originate from mathematical models. Careful differentiation and algebraic manipulation are necessary to obtain the correct result. Regular practice strengthens conceptual understanding and enables students to solve formation-based questions accurately during examinations.
The method of separation of variables is one of the simplest techniques for solving differential equations. In this approach, variables are rearranged so that terms involving one variable appear on one side of the equation and terms involving the other variable appear on the opposite side. After separation, both sides are integrated to obtain the solution. NCERT exercises include numerous examples that demonstrate this method. Students should focus on recognising equations that can be separated and applying integration correctly. Mastering this technique is important because it forms the basis for solving many standard differential equation problems.
Many students make mistakes while separating variables or performing integration incorrectly. Another common error is forgetting the constant of integration after solving the equation. Some students also simplify expressions incorrectly, leading to wrong final answers. In formation-based questions, careless differentiation often creates errors. NCERT exercises encourage a systematic approach that helps minimise such mistakes. Students should solve problems step by step, verify calculations, and check whether the final solution satisfies the original equation. Regular practice and attention to detail improve accuracy and confidence, helping students perform better in board examinations and competitive assessments.