RD Sharma Solutions to Class 12
FAQs on RD Sharma Class 12 Solutions Chapter 22 - Differential Equations (Ex 22.8) Exercise 22.8 - Free PDF
1. What specific topic is covered in RD Sharma Class 12 Maths Solutions, Chapter 22, Exercise 22.8?
Exercise 22.8 of RD Sharma Class 12 Maths Chapter 22 primarily focuses on solving Linear Differential Equations (LDEs). The problems in this section are typically of the standard form dy/dx + Py = Q, where P and Q are functions of x. Mastering this exercise requires understanding the method of using an Integrating Factor to find the general solution.
2. How do you solve a typical problem from Exercise 22.8 on Linear Differential Equations?
To solve a linear differential equation from Exercise 22.8, you should follow these steps:
Step 1: Arrange the given equation into the standard form dy/dx + Py = Q.
Step 2: Identify the functions P and Q from the equation.
Step 3: Calculate the Integrating Factor (I.F.) using the formula I.F. = e∫Pdx.
Step 4: Apply the general solution formula: y × (I.F.) = ∫(Q × I.F.)dx + C, where C is the constant of integration.
Step 5: Integrate the right-hand side and simplify to get the final solution.
3. What is an Integrating Factor (I.F.) and why is it crucial for solving the problems in Exercise 22.8?
An Integrating Factor (I.F.) is a function that is used to convert a non-exact differential equation into an exact one, which can then be easily integrated. For the linear differential equations in Exercise 22.8, the I.F. is crucial because multiplying the entire equation by it transforms the left side (dy/dx + Py) into the derivative of a product, specifically d/dx (y × I.F.). This strategic conversion simplifies the integration process, making it possible to find the general solution systematically.
4. What are the common mistakes to avoid when solving linear differential equations from RD Sharma Chapter 22, Exercise 22.8?
When solving problems from this exercise, students often make the following mistakes:
Incorrect Identification: Failing to correctly identify the functions P and Q after arranging the equation in standard form.
Integration Errors: Making calculation errors while finding the Integrating Factor (∫Pdx) or during the final integration step (∫(Q × I.F.)dx).
Forgetting the Constant: Forgetting to add the constant of integration, 'C', which is a critical part of the general solution.
Algebraic Mistakes: Simple algebraic errors during the final simplification of the solution.
5. How can I verify if my final solution to a differential equation from Exercise 22.8 is correct?
To verify your solution, you can use the method of differentiation. Take the general solution you have found (the equation relating y and x) and differentiate it with respect to x. Then, rearrange the resulting expression algebraically. If your solution is correct, you should be able to simplify this expression and arrive back at the original linear differential equation (dy/dx + Py = Q) that was given in the problem.
6. Are the methods in Vedantu's RD Sharma Solutions for Ex 22.8 reliable for the CBSE Class 12 board exams 2025-26?
Yes, the methods provided in Vedantu's solutions for Exercise 22.8 are fully aligned with the CBSE 2025-26 syllabus and exam pattern. Our subject matter experts have crafted these step-by-step solutions to ensure they follow the correct methodology and marking scheme prescribed by the board, making them a highly reliable resource for exam preparation.
7. How do these specific solutions for Exercise 22.8 contribute to mastering the entire Differential Equations chapter?
Mastering the linear differential equations in Exercise 22.8 builds a strong foundation for the entire chapter. This topic is one of the most important methods for solving differential equations and frequently appears in board exams. By understanding this specific method thoroughly, you can better tackle mixed-problem sets and application-based questions. For a complete overview of the chapter, you can refer to our main page for RD Sharma Class 12 Maths Solutions Chapter 22, which covers all exercises in detail.
