Separable differential equationsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

What makes \frac{dy}{dx}=f(x)g(y) separable?
Method of separation of variables?
Solution of \frac{dy}{dx}=ky?
General solution of \frac{dy}{dx}=2xy for y0?
Difference between general and particular solutions?
How do you separate \frac{dy}{dx}=xy+x?
\int\frac{1}{y^2}\,dy?
\int y^{-\frac12}\,dy?
What does a family of solution curves show?
How is acceleration written as a differential equation?
Distance from velocity v(t)?
Why state a domain of validity?

Exam questions on Separable differential equations

A curve satisfies the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}=2xy$ with $y>0$ .
Given that $y=3$ when $x=0$ , find the exact value of $y$ when $x=1$ .2 marks
The mass $m$ grams of a radioactive sample at time $t$ years satisfies $\frac{\mathrm{d}m}{\mathrm{d}t}=-0.05m$ . Initially the mass is $80$ g.
Find the time taken for the mass to fall to $40$ g, giving your answer in years to 3 significant figures.2 marks
A particle moves in a straight line. Its velocity $v$ m s $^{-1}$ at time $t$ seconds satisfies $\frac{\mathrm{d}v}{\mathrm{d}t}=-0.4v^2$ , and $v=5$ when $t=0$ .
Show that $v=\frac{5}{2t+1}$ .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).