# Differential Equations Class 12 Notes Mathematics Chapter 9

#### Chapter at a Glance

1. Differential Equation – An equation containing an independent variable and / or dependent variable and the differential coefficient of the dependent variable with respect to independent variable is called a differential equation.

2. Order of a Differential Equation – The degree of a differential equation is the order of the highest order derivative appearing in the equation.

3. Degree of a Differential Equation – Degree of a polynomial equation is defined only when it is a polynomial equation in derivatives.If a differential equation is a polynomial equation in derivatives, then highest power (positive integer index) of the highest order derivative involved in the given differential equation.

4. Solution of a Differential Equation – The solution of a differential equation is a relation between the variables involved, not involving the differential coefficients, such that this relation and derivatives obtained from it satisfy the given differential equation.

5. General Solution – The solution which contains as many as arbitrary constants as the order of the differential equation is called the general solution of the differential equation.

6. Particular Solution – Solution obtained by giving particular values to the arbitrary constants in the general solution of a differential equation is called a particular solution.

7. Formation of Differential Equations – If an equation representing a family of curves, contains n arbitrary constants, then we differentiate the given equation n times to obtain n more equations. Using all these equations, we eliminate the constants. The equation so obtained is the differential equation of order n for the family of given curves.

8. Homogeneous Differential Equation –

A differential equation of the form dy/dx = F (x, y) is said to be homogeneous if F (x, y)is a homogeneous function of degree zero.

The algorithm used to solve the homogeneous

9. Linear Differential Equation – A differential equation is known as first order linear differential equation, if the dependent variable (y) and its derivative appear in first

10. Differential Equations of the type

(i) Integrate both sides of the differential equation in (i) with respect to x to obtain a first order first degree differential equation.

(ii) Again integrate both sides of the first order differential equation obtained in (i) with respect to x.

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