Class 12 RS Aggarwal Chapter-19 Differential Equations with Variable Separable Solutions - Free PDF Download
FAQs on RS Aggarwal Class 12 Solutions Chapter-19 Differential Equations with Variable Separable
1. What is the first step to solve a problem from RS Aggarwal Class 12 Chapter 19 using the variable separable method?
The first and most crucial step is to rearrange the differential equation. You need to group all terms involving the variable y with dy on one side of the equation, and all terms involving the variable x with dx on the other side. This process isolates the variables, making them ready for integration.
2. How do the RS Aggarwal solutions help in finding the 'constant of integration' (C)?
After integrating both sides of the separated equation, the solutions show you how to add a single constant of integration, usually denoted by 'C'. For problems that ask for a particular solution, the steps then guide you on how to substitute the given initial values (e.g., y=a when x=b) to find the specific numeric value of C.
3. Are the methods in the RS Aggarwal solutions for Differential Equations aligned with the latest CBSE Class 12 syllabus?
Yes, the step-by-step methods provided for solving variable separable differential equations in these solutions are fully aligned with the CBSE curriculum for the 2025-26 academic year. They follow the prescribed methodology for finding both general and particular solutions, which is essential for board exams.
4. What is the key difference between a 'general solution' and a 'particular solution' in this chapter's problems?
A general solution of a differential equation contains an arbitrary constant (like 'C') and represents a whole family of curves. In contrast, a particular solution is derived from the general solution by using given conditions to find a specific value for 'C'. It represents a single, unique curve from that family that passes through a given point.
5. How can I tell if a differential equation can be solved using the variable separable method just by looking at it?
A first-order, first-degree differential equation can be solved by this method if you can express it in the form f(y) dy = g(x) dx. This means it must be possible to algebraically separate all functions of 'x' and 'dx' from all functions of 'y' and 'dy'. If you cannot completely isolate the variables in this way, another method is likely needed.
6. What is a common mistake to avoid when solving problems from RS Aggarwal Chapter 19?
A very common error is forgetting to add the constant of integration ('C') after integrating both sides. Leaving it out will result in an incorrect general solution. Another frequent mistake is making an algebraic error while separating the x and y terms, so always double-check your separation step before integrating.
7. Why is it necessary to integrate both sides after separating the variables in these equations?
The purpose of solving a differential equation is to find the original function y(x) from its derivative. By separating the variables into a form like g(y)dy = h(x)dx, you have isolated the changes in y with respect to the changes in x. Integration is the reverse of differentiation; applying it to both sides allows you to find the underlying relationship between y and x, which is the solution to the equation.
