# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-calculus-differential%20equations.html


## 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: \[ \mu(x) = e^{\int P(x)\,dx} \] \[ \frac{d}{dx}\big(\mu(x)y\big) = \mu(x)Q(x) \]

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