Differential Equations

2022 HCI P1 Q12 A cargo drone is used to unload First Aid kit at an accident location in a remote mountain area. The First Aid kit is unloaded vertically

2021 DHS Promo Q12 A fish pond has a surface area of $100$m$^{2}$. Past observations on the growth of algae in similar ponds estimates that the area, $A$m$^{2}$, of algae

2019 JPJC P2 Q4 A differential equation is given by $2{{u}^{2}}frac{{{text{d}}^{2}}x}{text{d}{{u}^{2}}}+4ufrac{text{d}x}{text{d}u}=15u+12$ where $x=0$ and $frac{text{d}x}{text{d}u}=1$ when $u=1$. By differentiating ${{u}^{2}}frac{text{d}x}{text{d}u}$ with respect to $u$, show that the solution of the

2018 AJC MYE P1 Q11 As part of the décor of a seafood restaurant, the owner places a fish tank filled with freshwater fish near the entrance to the restaurant.

2019 YIJC P1 Q10 A tank initially contains $2000$ litres of water and $20$kg of dissolved salt. Brine with $C$kg of salt per $1000$ litres is entering the tank at

2019 MI P2 Q3 (a) Find the general solution for the following differential equation $frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}={{text{e}}^{-5x+3}}+sin x$. [3] (b) By using the substitution $z=x+frac{text{d}y}{text{d}x}$, show that the following differential equation $frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}-frac{text{d}y}{text{d}x}-x+1=0$

ACJC Tutorial 24 Q7 (a) $frac{text{d}y}{text{d}x}-frac{y}{x}=1$ (use $y=vx$) (b) $frac{text{d}w}{text{d}s}+sin 2w={{sin }^{2}}w$ (use $z=tan w$) Suggested Handwritten and Video Solutions (a) (b) (a) (b)