Plus Two Maths Notes Chapter 9 Differential Equations is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 9 Differential Equations.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Notes |

Chapter | Chapter 9 |

Chapter Name | Differential Equations |

Category | Plus Two Kerala |

## Kerala Plus Two Maths Notes Chapter 9 Differential Equations

**Basic Concepts: order and Degree**

- order of a differential equation is the order of the highest order derivative occurring in the differential equation.
- The degree of a differential equation is the highest power (positive integer only) of the highest order derivative in it, after it is made free from radicals and fractions or quotients.
- The degree is defined in the given differential equation is a polynomial equation in its derivatives.

**Methods of Solving Differential Equation**

**I. Variable separable form:** An equation in the form M dx + N dy = o. where M = *f*(x) and N = g (y).

- General solution is ∫ Mdx+ ∫ Ndv = C

**II. Homogeneous differential equations:** An equation of the form = where *f*(x,y) and g (x.y) are homogeneous functions of the same degree in x and y.

**OR**

is also homogeneous.

In order to solve it. put y = vx

Then

After simplification, the given equation

reduces to variable separable form.

- If we are given an equation of the form It is also homogeneous. Here put x = vy then = .

**III. Linear differential equations:** An equation

in the form +Py = Q, where P, Q are constants or functions of x only

**OR**

an equation in the form +p_{1 }x = Q,

where P_{1} and Q_{1} are constants or functions of y only.

- I. OR
- General solution is

**OR**

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