An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable (variables) is called a differential equation.

The order of a differential equation is defined as the order of the highest order derivative of the dependent variable with respect to the independent variable involved in the given differential equation.

By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.

Order and degree (if defined) of a differential equation are always positive integers.

A differential equation is said to be linear if the dependent variable and all of its derivatives occurring in the equation occur only in the first degree and are not multiplied together.

A differential equation will be a non-linear differential equation if

(i) its degree is more than one;

(ii) any of the differential coefficients has exponents more than one;

(iii) products containing dependent variable and its differential coefficients are present.

Solutions of First-Order Linear Differential Equations are given below.

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NCERT Solutions – Class 12 – Mathematics – Chapter 9 – Exercise 9.2 – Differential Equations