Timothy Gan

2020 SAJC P2 Q3 The variables $x$ and $y$ are related by the differential equation $frac{text{d}y}{text{d}x}=frac{x-y}{x-y+1}$. (i) Solve the differential equation, using the substitution $u=x-y+1$, and show that the general

2020 TMJC P1 Q8 (i) Show that the differential equation $frac{text{d}y}{text{d}x}=5left( x-y right)$ may be reduced by the substitution $w=x-y$ to $frac{text{d}w}{text{d}x}=1-5w$. Hence find the general solution for $~y$ in

2020 RVHS P2 Q2 A particle moving in a liquid is such that after $t$ seconds, its velocity is $v$ ms$^{-1}$, $vne 0$. $v$ satisfies the differential equation $vfrac{text{d}v}{text{d}t}+2{{v}^{2}}=t{{text{e}}^{-2t}}$. (i)

2020 RI P1 Q3 (i) Prove that for $x>0$, the substitution $y=ux$ reduces the differential equation $left( y-x right)left( frac{text{d}y}{text{d}x}-frac{y}{x} right)={{y}^{2}}+2{{x}^{2}}$ to $left( frac{u}{{{u}^{2}}+2}-frac{1}{{{u}^{2}}+2} right)left( frac{text{d}u}{text{d}x} right)=1$. [2] (ii) Hence