IB Maths AI 5.8 Definitions

This page contains our IB Maths AI definitions for 5.8. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Introduction to differential equations'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Fundamentals Of Integration (HL)5.4: Advanced derivatives (HL)5.5: Further integration (HL)5.6: Applying integration (HL)5.7: Kinematics (HL)5.8: Introduction to differential equations (HL)5.9: Advanced differential equations

differential equation

An equation involving a function and one of its derivatives, so it describes how the function changes rather than giving the function directly.

Euler's method

A numerical technique that approximates the solution of '

\frac{dy}{dx}=f(x,y)

' from an initial point '

(x_0,y_0)

' using step size '

h

' and the updates '

x_{n+1}=x_n+h

' and '

y_{n+1}=y_n+hf(x_n,y_n)

first-order differential equation

A differential equation that involves only the first derivative, typically written as '

\frac{dy}{dx}

', and can be expressed in the form '

\frac{dy}{dx}=f(x,y)

homogeneous

Able to be written in the form '

\frac{dy}{dx}=f\left(\frac{y}{x}\right)

', so the right-hand side depends only on the ratio '

\frac{y}{x}

integrating factor

A function '

\mu(x)=e^{\int P(x)dx}

' used to solve '

y'+P(x)y=Q(x)

by making the left-hand side become '

\frac{d}{dx}\left(\mu y\right)

' after multiplication.

integration by substitution

Replacing one expression with another to simplify a differential equation, such as using '

y=vx

' so that '

\frac{dy}{dx}=v+x\frac{dv}{dx}

separation of variables

A solving technique that rewrites an equation like '

\frac{dy}{dx}=g(x)h(y)

' as '

\frac{1}{h(y)}\,dy=g(x)\,dx

' and then integrates both sides.

step size

The fixed increment '

h

' in the independent variable used in Euler's method to move from '

x_n

' to '

x_{n+1}=x_n+h

Next Up

You have completed the topic 5 definitions for IB Maths AI - continue with related resources below or explore the full IB Maths AI course from the IBO.

Explored IB Maths AI Definitions?

Get stuck into one of our other subjects!

Other subjects' Definitions

Biology

Chemistry

Physics

Maths AA

Join 85,000 students, across 130+ countries, in 500+ IB schools. That's half of the IB science graduates worldwide.

Start a 7d free trial