
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 12th, 2017, 11:59 PM  #1 
Newbie Joined: Jan 2014 Posts: 10 Thanks: 0  Constant solution
I want to find constant solutions of the differential equation $\frac{dy}{dx}=\frac{y^3}{x^2}2\frac{y}{x}$. I set $y=c$, where $c$ is a constant. Then $\frac{dy}{dx}=0$ and the differential equation becomes $0=\frac{c^3}{x^2}2\frac{c}{x}$ $\frac{c}{x}(\frac{c^2}{x}2)=0$ $c/x=0$ or $c^2/x2=0$ $c=0$ or $c^2=2x$ How to explain in words the equation $c^2=2x$ does not give any constant solution of the differential equation? 
November 13th, 2017, 01:06 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,407 Thanks: 480 Math Focus: Yet to find out. 
What do you mean you want to find a constant solution...? Are you trying to find a particular solution?

November 13th, 2017, 07:25 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,031 Thanks: 2342 Math Focus: Mainly analysis and algebra 
Duplicate post.

November 13th, 2017, 11:21 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,145 Thanks: 1418 
Differentiation with respect to $x$ requires that $x$ isn't a constant, so c² = 2$x$ isn't possible.


Tags 
constant, solution 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Constant pi  idontknow  Elementary Math  7  August 1st, 2017 01:23 PM 
Multiplying f(x) with constant and x with constant is same thing?  shahbaz200  Calculus  12  December 18th, 2016 01:50 AM 
Prove analytic function is constant, if argument is constant  ag07  Complex Analysis  6  December 4th, 2015 08:05 PM 
New Mathematical Constant: f  Algebra  12  October 14th, 2012 07:58 PM  
Is this a constant???  JamieStarr  Algebra  3  November 24th, 2010 04:18 PM 