/ Curriculum

Course Overview

8 chapters · H.K. Dass Engineering Mathematics §3.9–3.11

1

Introduction to Differential Equations

A DE is an equation relating an unknown function and its derivatives. Solutions are functions, not numbers.

2

Classification of Differential Equations

DEs are classified by type (ODE/PDE), order, degree, and linearity.

3

Formation of Differential Equations

n arbitrary constants → differentiate n times → eliminate constants → DE of order n.

4

Variable Separable Method

Rearrange so all y terms go left, all x terms go right, then integrate both sides.

5

Homogeneous Equations

A DE is homogeneous if f(x,y) depends only on y/x. Substitute v = y/x to convert to separable.

6

Linear DE — Integrating Factor Method

H.K. Dass — Section 3.9, p.147

Standard form: + P(x)y = Q(x). Multiply by integrating factor = .

7

Bernoulli's Equation

H.K. Dass — Section 3.10, p.150

Bernoulli form: + Py = Q. Substitute z = to linearize.

8

Exact Differential Equations

H.K. Dass — Section 3.11, p.154

A DE M dx + N dy = 0 is exact if = . Solution found by direct integration.