Turn on thread page Beta

General tips on making useful substitutions for differential equations? watch

    • Thread Starter

    Hi all, my maths isn't brilliant but usually if i'm given a substitution, I can figure out a solution fairly easily, for a ordinary differential equation

    But I'm very bad at figuring what a useful substitution to make is. Let me give a few examples, along with the substitution suggested in the answers, and can someone explain why that substituion is the logical choice? Thanks alot!

    suggested substitution:  u= y^{-4}

     \dfrac{dy}{dx}+y=y^2 (cos(x)-sin(x))
    suggested substitution:  u= y^{-1}

    Can't see the logic :confused:

    I think both these equations are of the form described here

    Basically if you have something of the form  \frac{dy}{dx} + P(x)y = Q(x)y^n then substitute  u = y^{-(n-1)} .

    There are probably other specific types of ODEs which have a specific useful substitution, but I can't remember them if I covered them in my course. We did cover these Bernoulli ones though.
Submit reply
Turn on thread page Beta
Updated: January 28, 2010

University open days

  • University of Exeter
    Undergraduate Open Days - Exeter Campus Undergraduate
    Wed, 24 Oct '18
  • University of Bradford
    Faculty of Health Studies Postgraduate
    Wed, 24 Oct '18
  • Northumbria University
    All faculties Undergraduate
    Wed, 24 Oct '18
Who is most responsible for your success at university
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way


Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.