First order linear differential equationsEdexcel International A Level Further Maths: Mind map

Standard form

Integrating factor

First order linear

integrating factor

\frac{dy}{dx}+Py=Q

I=e^{\int P}

Solving

Particular solution

Modelling

Exam questions on First order linear differential equations

Consider the differential equation $\frac{dy}{dx}+3y=e^{2x}$ .
Find the general solution.2 marks
Consider the differential equation $x\frac{dy}{dx}-2y=x^3$ for $x>0$ .
Find the general solution.2 marks
Consider the differential equation $\frac{dy}{dx}+y\tan x=\sec x$ for $0<x<\frac{\pi}{2}$ .
Show that the integrating factor is $\sec x$ .3 marks

See the full worksheet

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).