Maths with Lemon

Differential equations

"Science is a differential equation. Religion is a boundary condition. "

Alan Turing

Differential Equations

What you have to know:

The derivatives of all known functions
(If not, check this lesson)
You must be able to integrate
(If not, check this lesson)
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Check out this presentation.

3. Watch this solved problem video.

Slope fields

What you have to know:

How to plot linear graphs.
(If not, check this lesson)

Key Points

1. Watch the video:

Euler's Method

What you have to know:

How to plot linear graphs
(If not, check this lesson)
To see how to solve this exercise using Ti84 check this file
(Check the file)

Key Points

1. Watch the video:

2. Check out this presentation.

Extra

Material and references:

Hodder Book HL(ISBN: 9781510462366) :
11A, 11B, 11C

Key Points

2. You should know that differential equations of the form \[ \frac{dy}{dx} = f(x)g(y) \] can be solved by separation of variables \[ \int \frac{1}{g(y)} \, dy = \int f(x) \, dx \]

3. You should know that a homogeneous differential equation can be written in the form \( \frac{dy}{dx} = f\!\left(\frac{y}{x}\right) \) and can be solved using the substitution \( y = vx \).

4. You should know that first order linear differential equations are of the form \[ \frac{dy}{dx} + P(x)y = Q(x) \] They can be solved by using an integrating factor: \[ \mu(x) = e^{\int P(x)\,dx} \] \[ \frac{d}{dx}\big(\mu(x)y\big) = \mu(x)Q(x) \]

IB Past Paper Problems

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