# 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-separable## Rs 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 |