Solving a diff eq by substituion

  • Thread starter Thread starter shemer77
  • Start date Start date
  • Tags Tags
    Diff eq
shemer77
Messages
96
Reaction score
0

Homework Statement


x*y2(dy/dx)=y3-x3
solve the problem

Homework Equations





The Attempt at a Solution


My answer was (x3/3)+c=y/x
there is no answer in the back of the book for this one so i just want to make sure i got it right
 
Physics news on Phys.org
shemer77 said:

Homework Statement


x*y2(dy/dx)=y3-x3
solve the problem

Homework Equations



The Attempt at a Solution


My answer was (x3/3)+c=y/x
there is no answer in the back of the book for this one so i just want to make sure i got it right
Solve your result for y. Then, take the derivative & plug it into the given equation. See if you get equality.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

Similar threads

Replies
3
Views
2K
Replies
4
Views
3K
Replies
4
Views
1K
Replies
9
Views
3K
Replies
5
Views
2K
Replies
3
Views
2K
Replies
4
Views
1K
Back
Top