Separable first order differential equationsEdexcel International A Level Maths: Mind map

Exam questions on Separable first order differential equations

1. A curve satisfies the differential equation $\frac{dy}{dx}=\frac{x}{y}$ with $y>0$.
   Given also that $y=3$ when $x=2$, find the value of $y$ when $x=4$.2 marks
2. Water drains from a tank. The depth $h$ metres of water at time $t$ minutes satisfies $\frac{dh}{dt}=-k\sqrt{h}$, where $k$ is a positive constant. Initially $h=4$, and after 10 minutes $h=1$.
   Find the time taken for the tank to empty completely.2 marks
3. The curve $C$ satisfies $\frac{dy}{dx}=\frac{2y+1}{x}$ for $x>0$, and passes through the point $(1,2)$.
   Find the general solution of the differential equation, giving your answer in the form $\ln|2y+1|=f(x)$.3 marks