Differential Equations

2021 HCI P1 Q10 A flu virus is spreading in a community which has a fixed population of $N$ people. Scientists discover that at time $t$ weeks from the beginning,

2021 ACJC P1 Q10 The Gompertz differential equation provides a good model for gauging lung cancer growth. The differential equation is given as $frac{text{d}V}{text{d}t}=aVln left( frac{K}{V} right)$, where $V$mm$^{3}$ is

2021 EJC P1 Q5 (a) (i) It is given that $yfrac{text{d}y}{text{d}x}+x=sqrt{{{x}^{2}}+{{y}^{2}}}$. Using the substitution $w={{x}^{2}}+{{y}^{2}}$, show that the differential equation can be transformed to $frac{text{d}w}{text{d}x}=text{f}left( w right)$, where the function

2021 MI P1 Q3 (i) It is given that ${{x}^{2}}frac{text{d}y}{text{d}x}-3xy+4=0$. Using the substitution $y=u{{x}^{3}}$, show that the differential equation can be transformed to $frac{text{d}u}{text{d}x}=frac{c}{{{x}^{5}}}$, where $c$ is a constant to

2021 NYJC P2 Q2 Many industries use rectangular tanks to handle their water, wastewater and chemical storage and processing needs. Because of their shape, rectangular tanks can offer tremendous cost

2014 NJC P1 Q11 A freshly brewed cup of coffee has an initial temperature $95{}^circ C$. It is placed in a room where the temperature is a constant at $20{}^circ

2020 TJC P1 Q11 In a research laboratory, scientists carry out experiments to produce a new substance $C$. $C$ is produced when two substances $A$ and $B$ are reacted together

2008 PJC P1 Q8 The quantities $x$ and $y$ are related by the differential equation $xfrac{text{d}y}{text{d}x}=yleft( 1-x-y right)$. (i) Show that this differential equation may be reducced by means of

2011 RVHS Q12 [Modified] (a) (i) Find the general solution of the differential equation $frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}=sec xtan x$. [2] (ii) Find the particular solution of the differential equation for which $y=2$