Differential Equations — Part 1: Order, degree, formation and separable equations: visual lesson, ISC Class 12 Mathematics

Lesson

Differential Equations, Part 1

An equation whose unknown is a function, linked to its own rate of change.

In this lesson you will

Solutions of $\dfrac{dy}{dx} = \dfrac{y}{2}$: one equation, a whole family of curves.

Concept

Part 1 at a glance.

Concept

Order: the highest derivative present. Degree: the power of that derivative, once the equation is a polynomial in the derivatives.

Order: highest derivative. Degree: its power, once the equation is a polynomial in the derivatives.
Equation	Order	Degree
$\dfrac{dy}{dx} + 4y = x$	$1$	$1$
$\left(\dfrac{d^2y}{dx^2}\right)^3 + \dfrac{dy}{dx} = 0$	$2$	$3$
$\dfrac{d^3y}{dx^3} + \left(\dfrac{dy}{dx}\right)^5 = \sin x$	$3$	$1$
$\dfrac{d^2y}{dx^2} + \cos\left(\dfrac{dy}{dx}\right) = 0$	$2$	not defined