RS Aggarwal Class 12 Differential equations with variable separable PDF
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What are Differential equations with variable separable?
A differential equation is said to be variable separable if it can be written in the form:
dy/dx = f(x)g(y)
where f(x) and g(y) are functions of x and y respectively.
Solving a variable separable differential equation involves separating the variables x and y, by dividing both sides of the equation by g(y) and then multiplying both sides by dx to get:
dx/f(x) = dy/g(y)
This equation can then be integrated on both sides to find the general solution of the differential equation.
An example of a variable separable differential equation is: dy/dx = x*y^2
This can be solved by dividing both sides by y^2 and then multiplying both sides by dx to get:
dx/x = dy/(y^2)
Integrating both sides we get:
∫dx/x = ∫dy/(y^2) + c
Where c is the constant of integration.
This method of solving variable separable differential equations is particularly useful when the functions f(x) and g(y) can be easily integrated, or when a general solution is needed rather than a specific solution.
CH-19-Differential-equations-with-variable-separableRs Aggarwal Class 12 PDF (All Chapters PDF)
| Chapter no. | chapter name | |
|---|---|---|
| 1 | Relations | Download |
| 2 | Functions | Download |
| 3 | Binary Operations | Download |
| 4 | Inverse Trigonometric Functions | Download |
| 5 | Matrices | Download |
| 6 | Determinants | Download |
| 7 | Adjoint and Inverse Of Matrix | Download |
| 8 | System of Linear Equations | Download |
| 9 | Continuity and Differentiability | Download |
| 10 | Differentiations | Download |
| 11 | Applications of Derivatives | Download |
| 12 | Indefinite Integrals | Download |
| 13 | Methods of integration | Download |
| 14 | Some Special integrals | Download |
| 15 | Integration using Partial Functions | Download |
| 16 | Definite integrals | Download |
| 17 | Area of Bounded Regions | Download |
| 18 | Differential equations and their formations | Download |
| 19 | Differential equations with variable separable | Download |
| 20 | Homogeneous Integral equations | Download |
| 21 | Linear Differential equations | Download |
| 22 | Vectors And Their Properties | Download |
| 23 | Scalar, or Dot product of Vectors | Download |
| 24 | Cross or vector products of Vector | Download |
| 25 | Product of three vectors | Download |
| 26 | Fundamental Concepts of 3D Geometry | Download |
| 27 | Straight Line in Space | Download |
| 28 | The Plane | Download |
| 29 | Probability | Download |
| 30 | Bayes’s Theorem and its Applications | Download |
| 31 | Probability Distribution | Download |
| 32 | Binomial Distributions | Download |
| 33 | Linear Programming | Download |