First order equations and integrating factorsAQA A-Level Further Maths: Mind map

Standard form

The method

First-order equations

I1 to I3

integrating factorgeneral solution

Simplifying I

Solutions

Modelling

Exam questions on First order equations and integrating factors

$\frac{dy}{dx}+\frac{3}{x}y=x^2$ , for $x>0$ .
Find the general solution, giving $y$ in terms of $x$ .2 marks
$\frac{dy}{dx}-2y=e^{3x}$ .
Given that $y=3$ when $x=0$ , find $y$ in terms of $x$ .2 marks
$\frac{dy}{dx}+y\tan x=\cos x$ , for $-\frac{\pi}{2}<x<\frac{\pi}{2}$ .
Show that the general solution is $y=(x+c)\cos x$ .3 marks

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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).