Mathematics AI: DIFFERENTIAL EQUATIONS Topical Past Paper Questions

[Maximum mark: 29] In this question researchers are trying to find the most accurate model to use when modelling a population of wolves. Historically, a population of wolves in an area had a stable size of 200. After some years of disruption, the population was reduced to 40 wolv…

[Maximum mark: 4] Consider the differential equation $ \frac{dy}{dx}=3x-y+1 $. (a) Find the equation of the tangent to the solution curve at the point $ (-1, -1) $ in the form $ ax + by + c = 0 $. The slope field for this differential equation is shown in the following diagram. […

[Maximum mark:5] An electrical circuit contains a capacitor. The charge on the capacitor, $q$ Coulomb's time $t$ seconds, satisfies the differential equation $$ \frac{\mathrm{d}^{2}q}{\mathrm{d}t^{2}}+5\frac{\mathrm{d}q}{\mathrm{d}t}+20q=200. $$ Initially $q=1$ and $\frac{\mathrm…