Separable first order differential equationsEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

What does it mean for a first order differential equation to be separable?
Method for solving a separable equation?
What is the general solution of a differential equation?
What is a particular solution?
Solve \frac{dy}{dx}=ky.
Integral of \frac{1}{2y+1} with respect to y?
Integral of y^{-1/2} with respect to y?
How do you separate \frac{dy}{dx}=e^{x-y}?
Why include only one constant of integration?
Newton's law of cooling in differential form, and its solution?
How do you find k in a modelling question?
How can you check a solution?

Exam questions on Separable first order differential equations

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).