Substitution differential equation problem

  • Thread starter Michels10
  • Start date
  • #1
18
0
Solve y' = y/x + 1/y


I get a similar answer to the correct one but I believe I am making a substitution error. Here is my attempt:




dy/dx = y/x + 1/y

set v = y/x

equation now becomes: v + x(dv/dx) = v + 1/(x*v)

reduces to: dv/dx = 1/(x^2 * v)

Now the equation is seperable, so I seperate and take the integral of both sides yielding:

v = (sqrt(-2) * sqrt(x*c - 1))/sqrt(x)

--even if i substitute v = y/x back in it doesn't come out to be the correct solution of:

y = sqrt(x) * sqrt(x*c -2)



Any insight would be great!
 

Answers and Replies

  • #2
18
0
Nevermind, solved it. Needed to substitute v=y^2.

Thanks!
 

Related Threads on Substitution differential equation problem

Replies
7
Views
3K
  • Last Post
Replies
1
Views
796
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
805
Replies
8
Views
2K
Replies
2
Views
4K
Replies
13
Views
988
Replies
2
Views
11K
Replies
2
Views
10K
Top