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).