Differential Equations

2022 MI J2 MYE P1 Q9 A team of scientists is studying the change in population of a particular species of fish in a lake. It is observed that the

2022 ASRJC J2 MYCT P1 Q11 A patient is injected with $150$mg of a drug for treatment of a disease. Every $8$ hours, $15%$ of the drug passes out of

2019 TJC P1 Q11 The daily food calories, $L$, taken in by a human body are partly used to fulfil the daily requirements of the body. The daily requirements is

2022 CJC J2 MYE P1 Q3 (i) Show that the substitution $v=x+4y+3$ reduces the differential equation $frac{text{d}y}{text{d}x}={{left( x+4y+3 right)}^{2}}$ to $frac{text{d}v}{text{d}x}=1+4{{v}^{2}}$. [2] (ii) Hence, find the general solution of the

2022 ASRJC J2 MYCT P1 Q7 (b) Using the substitution $y=u{{x}^{2}}$, show that the differential equation $frac{text{d}y}{text{d}x}=frac{2y}{x}+frac{{{x}^{2}}left( 1-2x right)}{2left( 1+4{{x}^{2}} right)}$ can be reduced to $frac{text{d}u}{text{d}x}=frac{1-2x}{2left( 1+4{{x}^{2}} right)}$. Hence solve

2016 NYJC MYE P1 Q1 Show that the differential equation $frac{text{d}y}{text{d}x}-ytan x=2sin x{{text{e}}^{cos x}}$ may be reduced by means of the substitution $y=usec x$ to $frac{text{d}u}{text{d}x}=2sin xcos x{{text{e}}^{cos x}}$. Hence

Home 2012 AJC MYE P1 Q5 Two variables $x$ and $y$ are related by the differential equation $frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}=frac{2x}{sqrt{1-4{{x}^{2}}}}$.Given that $y=1$ and $frac{text{d}y}{text{d}x}=-frac{1}{2}$ when $x=0$. (i) Show that $frac{text{d}y}{text{d}x}=asqrt{1-4{{x}^{2}}}$ where $a$

ACJC Tutorial 24 Q5 Using the substitution $z=theta -y$ , solve the differential equation $frac{text{d}y}{text{d}theta }=1-cos left( theta -y right)$. Suggested Video and handwritten Solutions

2019 HCI P2 Q4 (a) When studying a colony of bugs, a scientist found that the birth rate of the bugs is inversely proportional to its population and the death