RD Sharma Class 12 Solutions Chapter 22 – Differential Equations ( EX 22.11 ) Exercise 22.11 – Free PDF
FAQs on RD Sharma Class 12 Solutions Chapter 22 – Differential Equations
1. How do the Vedantu RD Sharma Solutions for Class 12 Chapter 22 help in solving differential equations?
The RD Sharma Solutions for Class 12 Chapter 22 provide a detailed, step-by-step guide to solving every problem in the textbook. They are designed to help students understand the correct methodology for each type of differential equation, from identifying the order and degree to applying methods like variable separable, homogeneous equations, and linear differential equations. This ensures students can build a strong foundation and verify their own answers.
2. What is the correct method to find the order and degree of a differential equation as explained in RD Sharma solutions?
To find the order and degree of a differential equation, the solutions guide you through a two-step process:
- Order: Identify the highest order derivative present in the equation. For example, if the highest derivative is d²y/dx², the order is 2.
- Degree: After ensuring the equation is a polynomial in its derivatives (free from radicals and fractions in derivatives), the degree is the highest power of the highest order derivative. If the equation cannot be expressed as a polynomial in its derivatives, the degree is not defined.
3. Why is identifying the correct type of differential equation (variable separable, homogeneous, or linear) the most crucial first step?
Identifying the correct type of a first-order, first-degree differential equation is crucial because the solution method directly depends on its classification. Applying the wrong technique will lead to an incorrect solution or a dead end. For instance, you cannot solve a linear differential equation by separating variables. The RD Sharma solutions help you practise this identification, which is the key to solving problems efficiently and accurately.
4. What are the key steps to solve a linear differential equation of the form dy/dx + Py = Q using the methods in RD Sharma?
The solutions in RD Sharma for linear differential equations consistently follow these key steps:
- First, ensure the equation is in the standard form dy/dx + Py = Q.
- Identify the functions P and Q.
- Calculate the Integrating Factor (I.F.) using the formula I.F. = e∫Pdx.
- Apply the general solution formula: y × (I.F.) = ∫(Q × I.F.)dx + C, where C is the constant of integration.
- Solve the integral on the right-hand side to find the final solution.
5. What are common mistakes when finding the integrating factor (I.F.), and how do these solutions help avoid them?
A common mistake is an error in the integration of 'P' when calculating the Integrating Factor (I.F. = e∫Pdx). Students often forget to handle negative signs or misapply integration rules for logarithmic or trigonometric functions. The RD Sharma solutions provide a verified, step-by-step calculation of the I.F. for every problem, allowing you to cross-check your work and master the integration process, which is critical for getting the correct final answer.
6. How does practising the formation of differential equations from RD Sharma Chapter 22 strengthen conceptual understanding for the CBSE 2025-26 exam?
Forming a differential equation from a given solution is the reverse process of solving one. This requires eliminating arbitrary constants through differentiation. Practising these problems from RD Sharma builds a deeper understanding of the relationship between a function and its derivatives. This skill is essential for tackling Higher Order Thinking Skills (HOTS) questions in the CBSE board exam, as it shows you understand the concepts, not just the solution formulas.
7. Beyond finding the final answer, what is the importance of the step-by-step methodology in the RD Sharma solutions for this chapter?
The step-by-step methodology is more important than the final answer because the CBSE 2025-26 evaluation pattern awards marks for each correct step. Understanding the method helps you tackle unfamiliar problems in exams, reduces the chance of careless errors, and ensures you can demonstrate your full understanding even if a final calculation is incorrect. The solutions train you to think methodically, a crucial skill for scoring well in calculus.
