Preparation for Class 12 with RD Sharma Solutions
FAQs on RD Sharma Solutions for Class 12 Maths Chapter 22 - Differential Equations - Free PDF Download
1. Why are Vedantu’s RD Sharma Solutions for Class 12 Maths Chapter 22 considered a reliable resource for board exam preparation?
Vedantu's RD Sharma Solutions for Class 12 Maths Chapter 22 are highly reliable because they provide accurate, step-by-step answers for every question in the textbook. Prepared by subject matter experts, these solutions clarify complex concepts in Differential Equations, help students verify their methods, and offer a structured approach to problem-solving that aligns with the CBSE marking scheme for the 2025-26 session.
2. How do the RD Sharma solutions explain the method to find the order and degree of a differential equation?
The solutions provide a clear methodology. To find the order, you identify the highest derivative (like d²y/dx² or d³y/dx³) present in the equation. To find the degree, you first ensure the equation is a polynomial in its derivatives (free from radicals or fractions involving derivatives). The degree is then the highest power of the highest-order derivative. The solutions provide numerous examples to solidify this concept.
3. What are the key steps for solving a linear differential equation of the form dy/dx + Py = Q, as detailed in the solutions?
The RD Sharma solutions break down the process into clear, manageable steps:
- First, identify the functions P and Q by comparing the given equation with the standard form.
- Next, calculate the Integrating Factor (I.F.) using the formula I.F. = e∫P dx.
- Finally, apply the general solution formula: y × (I.F.) = ∫(Q × I.F.) dx + C, where C is the arbitrary constant of integration.
4. What is the fundamental difference between a general solution and a particular solution in differential equations?
A general solution of a differential equation contains arbitrary constants (like 'C') and represents a whole family of curves that satisfy the equation. In contrast, a particular solution is derived from the general solution by applying specific, given conditions (e.g., y=1 when x=0). This process eliminates the arbitrary constant, resulting in a unique equation that represents a single, specific curve from that family.
5. How can I identify if a differential equation is homogeneous, and what is a common mistake to avoid when solving it?
A first-order, first-degree differential equation is identified as homogeneous if it can be expressed in the form dy/dx = F(y/x). The key is that all terms are of the same degree. A common mistake students make is during the substitution step. After substituting y = vx, you must also substitute dy/dx = v + x(dv/dx). Forgetting to use the product rule for the derivative substitution is a frequent source of errors.
6. Why is finding an Integrating Factor (I.F.) crucial for linear differential equations but not for homogeneous or variable-separable types?
The Integrating Factor is a unique function designed to make a non-exact linear differential equation exact, allowing it to be solved by reversing the product rule of differentiation. This step is unnecessary for other types because their structures are different. The variable-separable method works by simply isolating variables on opposite sides of the equation. The homogeneous method uses a substitution (y=vx) to transform the equation into a variable-separable form, which can then be solved directly without an I.F.
7. What types of problems on forming differential equations are covered in RD Sharma Class 12 Chapter 22?
RD Sharma Chapter 22 provides extensive practice in forming differential equations. The problems typically involve eliminating arbitrary constants from a given equation representing a family of curves (e.g., y = mx + c). It also includes questions based on geometric properties, such as finding the differential equation for a family of circles passing through the origin or a family of parabolas with a specific axis, which helps build a deeper conceptual understanding for the CBSE 2025-26 board exams.
