Solving a Murder Mystery

# Differential Equations: Solving a Murder Mystery

How to use differential equations to solve a Gruffalo inspired murder mystery.

The below video was originally produced as a Seren Network Masterclass organised by the Port Neath Talbot, Powys and Bridgend Hub.

## Exercise:

Test your understanding of the video with the following.

1. Solve the differential equation $$\frac{dy}{dx} + 3x^2 y =6x^2$$

As this is already in the standard form of $$\frac{dy}{dx} + P(x)y = Q(x)$$ you can start by multiplying both sides by the integrating factor $$I(x) = e ^{\int P(x)dx}$$

$$y = 2 + Ce^{-x^3}$$

2. After 10 minutes a cup of coffee has cooled from 100°C to 40°C. The room temperature is 25°C. How much longer will it take for the coffee to cool to 35°C?

You will need to know Newton's Rule of Cooling (see above video).

$$\frac{10ln(\frac{15}{2})}{ln5} \approx 2.52 \textup{ minutes}$$