RD Sharma Solutions for Class 12 Maths Chapter 22 - Differential Equations - Free PDF Download
FAQs on RD Sharma Class 12 Maths Solutions Chapter 22 - Differential Equations
1. Where can I find clear, step-by-step solutions for all exercises in RD Sharma Class 12 Maths Chapter 22, Differential Equations?
You can find detailed, exercise-wise solutions for RD Sharma Class 12 Maths Chapter 22 (Differential Equations) right here on this Vedantu page. Our subject matter experts have solved every question according to the latest CBSE guidelines for the 2025-26 session, ensuring you understand the correct methodology for solving each type of differential equation.
2. How should I use these RD Sharma solutions for Chapter 22 to effectively prepare for my board exams?
For best results, first attempt to solve the problems from the RD Sharma textbook on your own. Use these Vedantu solutions as a guide to verify your method, check your final answer, or understand the steps if you get stuck. This approach helps in building problem-solving skills rather than just memorising solutions.
3. What is the correct method to determine the order and degree of a differential equation as per the problems in this chapter?
To find the order and degree, first ensure the differential equation is a polynomial equation in its derivatives (i.e., free from radicals or fractional powers of derivatives). The order is the highest order of the derivative present in the equation. The degree is the highest power of that highest-order derivative.
4. What are the main types of first-order, first-degree differential equations covered in the solutions for RD Sharma Chapter 22?
The solutions for this chapter primarily cover the methods for solving three main types of first-order, first-degree differential equations, which are aligned with the CBSE syllabus:
- Equations solvable by the variable separable method.
- Homogeneous differential equations.
- Linear differential equations of the form dy/dx + Py = Q.
5. How can I identify if a differential equation is homogeneous, and why does the substitution y = vx work for solving it?
A differential equation is homogeneous if it can be expressed in the form dy/dx = F(y/x) or G(x/y). The substitution y = vx is effective because it transforms the equation into a new one involving variables v and x. This new equation can always be solved using the variable separable method, simplifying the entire process.
6. Why is calculating the Integrating Factor (I.F.) essential for solving linear differential equations?
The Integrating Factor (I.F.) is a crucial function that, when multiplied with the entire linear differential equation (dy/dx + Py = Q), converts the left side into the derivative of a product, specifically d/dx (y × I.F.). This transformation makes the equation directly integrable, allowing you to find the solution systematically.
7. What is the fundamental difference between a 'general solution' and a 'particular solution' in the context of Chapter 22?
A general solution of a differential equation includes an arbitrary constant (e.g., 'C') and represents a family of curves. A particular solution is derived from the general solution by applying specific initial conditions or boundary values (e.g., y=2 when x=1). This process determines a specific value for 'C', resulting in a single, unique solution curve.
8. While using the solutions, what is a common mistake students make when solving problems using the variable separable method?
A common mistake is incorrectly separating the variables. Students must ensure that all terms involving 'y' are grouped with 'dy' and all terms involving 'x' are grouped with 'dx' on opposite sides of the equation before integration. Another frequent error is forgetting to add the constant of integration, 'C', after integrating both sides, which is essential for finding the general solution.
