Differential Equations

2022 SAJC P1 Q7 The rate of temperature loss of an animal corpse can be estimated using Newton’s Law of Cooling, which states that the rate of change of temperature

2022 ASRJC P1 Q11 The cylindrical tank in a research laboratory has a cross-sectional area of $4$ m$^{2}$. To cool the tank, water is pumped in and out of the

2022 ACJC P1 Q11 With the proliferation of online social network, sociologists recognised a phenomenon called social diffusion which is the spreading of a piece of information through the population.

2022 VJC P1 Q11 A tank contains $500$ litres of water in which $100$ g of a poisonous chemical called Prokrastenate is dissolved. A solution containing $0.1$ g of Prokrastenate

2022 DHS P1 Q10 An object is moving from rest in a gas chamber and $t$ seconds later, its velocity $v$ metres per second satisfies the differential equation $frac{text{d}v}{text{d}t}=5-0.2{{v}^{2}}$ It

2023 CJC P2 Q3 Following the popularity of the action role-playing game, Ginseng Impact, three years ago, developers have developed a strategy game, Ginseng Impactful. The number of people who

2010 ACJC P1 Q12 (i) Show, by using the substitution $w=frac{y}{{{t}^{2}}}$, that the general solution of the differential equation $tfrac{text{d}w}{text{d}t}={{w}^{2}}{{t}^{3}}+2wt-2w$ is $w=frac{1}{{{t}^{2}}}left( frac{2A{{e}^{2t}}}{1-A{{e}^{2t}}} right)$. [5] (ii) Find the particular solution,

2022 NYJC P1 Q11 In a chemical reaction, two substances $A$ and $B$ are combined to form a new substance $C$. The initial masses of $A$, $B$and $C$ are $8$,

2021 DHS Promo Q3 It is given that $xfrac{text{d}y}{text{d}x}=2y-8$. (i) Using the substitution $y=u{{x}^{2}}$ or otherwise, solve the differential equation giving your answer in the form $y=text{f}left( x right)$. [4]

2022 MI P1 Q2 (i) Show, by means of the substitution $w={{x}^{2}}y$, that the differential equation $2y+xfrac{text{d}y}{text{d}x}=-frac{5}{{{x}^{4}}}$ can be reduced to the form $frac{text{d}w}{text{d}x}=-frac{5}{{{x}^{3}}}$. [3] (ii) Hence, given that $y=3$