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NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Exercise 9.2
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Chapter 9 – Differential Equations Exercise 9.2
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Ans – The number of constants in the general solution of a differential equation of order n is equal to the order of the differential equation. Hence, the general equation of a fourth-order differential equation contains four constants. Therefore, option D is the correct answer.
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Ans – When the general solution’s arbitrary constant takes on a unique value, it becomes the problem’s particular solution. Applying boundary conditions yields the particular solution to a differential equation. It is well known that no arbitrary constants are found in any given solution of a differential equation. Hence, the correct answer is option D.
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Class 12 Maths Chapter 9 – Differential Equations: All Exercises
| Exercise | Link |
|---|---|
| Exercise 9.1 | View Solutions |
| Exercise 9.3 | View Solutions |
| Exercise 9.4 | View Solutions |
| Exercise 9.5 | View Solutions |
Class 12 Differential Equations- Exercise 9.2 Overview
Exercise 9.2 of Chapter 9 in the Class 12 NCERT Maths book concentrates on solving first-order differential equations by separating variables, a basic yet effective method. Reiterating integration and equation-solving techniques, this method helps students grasp how to simplify difficult-looking differential equations into integrable forms.
Students will learn in Chapter 9 Class 12 NCERT Solutions Exercise 9.2 how to determine the general or particular solutions as needed, separate variables algebraically, and integrate both sides. These challenges are meant to deepen your knowledge of how differential equations connect to the idea of rate of change, a notion applied often in economics, physics, and biology.
Guiding you through the logic of separation and integration, our Differential Equations Class 12 NCERT Solutions Exercise 9.2 presents comprehensive, step-by-step approaches for every question. Visual learners and those who find it difficult to link theory to real-world problem-solving will find particular benefit from these justifications.
This material is still fundamental in Class 12 calculus and has considerable relevance for students getting ready for competitive tests like JEE or CUET with the changes for the 2025 NCERT syllabus. Completing this assignment will provide you with a useful method for addressing problems and a better knowledge of the applications of differential equations in the real world.
FAQs – Differential Equations Class 12 Exercise 9.2 NCERT
Using the technique of separation of variables—that is, writing the equation so that each variable and its differential are on opposite sides—this exercise concentrates on solving first-order differential equations.
Indeed, you have to integrate both sides once the variables are separated in order to get the differential equation’s general solution.
You will run across rational expressions, exponential functions, and polynomials. Accurate solution of these requires fundamental integration methods.
Indeed, always include “+ C” in your general solution unless the problem especially requests for a specific solution with certain criteria.