Mathematics AA: 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 wolve…

[Maximum mark: 9] Consider the differential equation $ \frac{dy}{dx}=\frac{4-y}{10} $, where y=2 when x=0. (a) Use Euler's method with a step size of 0.1 to find an approximation for y when x = 0.5. Give your answer correct to four significant figures. (b) By solving the differen…

[Maximum mark: 10] Consider the homogeneous differential equation $ \frac{dy}{dx}=\frac{y^{2}-2x^{2}}{xy} $, where $ x, y \neq 0 $. It is given that y=2 when x=1. (a) By using the substitution $y = vx$, solve the differential equation. Give your answer in the form $y^{2} = f(x)$.…