Further Mathematics 7367: Differential Equations Topical Past Paper Questions

Solve the differential equation $$\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}+4\frac{\mathrm{d}y}{\mathrm{d}x}-45y=21\mathrm{e}^{5x}-0.3x+27x^{2}$$ given that $y=\frac{37}{225}$ and $\frac{\mathrm{d}y}{\mathrm{d}x}=0$ when $x=0$

Find the general solution of the differential equation $$\frac{d^2y}{dx^2}-3\frac{dy}{dx}-4y=\cos 2x+5x$$ [9 marks]

In a colony of seabirds, there are y birds at time t years. (a) The rate of reduction in the number of birds due to birds dying or leaving the colony is proportional to the number of birds. In one year the reduction in the number of birds due to birds dying or leaving the colony…