#### 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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- NCERT Solutions for class 12th Mathematics Chapter 9 Differential Equations