Can substitution be used to solve this homogeneous DE?

  • Thread starter Thread starter abrowaqas
  • Start date Start date
  • Tags Tags
    Homogeneous
Click For Summary
The discussion revolves around solving the homogeneous differential equation xcos(y/x)(ydx+xdy) = ysin(y/x)(xdy-ydx) using substitution. The user begins by letting y = vx and attempts to find its derivative for substitution into the equation. However, they encounter difficulties in simplifying the resulting equation to find a suitable integral. The simplified form of the equation is dx/x = [(vtanv-1)/2v]dv, but the user seeks assistance in progressing further. The conversation highlights the challenges of applying substitution methods in this context.
abrowaqas
Messages
113
Reaction score
0
xcos(y/x)(ydx+xdy) = ysin(y/x)(xdy-ydx)

I have started to it by
Letting
y=vx
And then
Find it's derivative put their in equation
. But the equation afterwards cannot come for finding suitable integral.
Kindly help.
 
Physics news on Phys.org
The equation becomes dx/x =[(vtanv-1)/2v]dv on simplification.
 

Similar threads

MHB How can I solve a non-homogeneous equation using substitution?
  • · Replies 1 ·
Replies
1
Views
2K
MHB How to solve a differential equation using substitution?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Stuck on solving a non homogenous (linear) PDE
  • · Replies 36 ·
2
Replies
36
Views
5K
Line element in cylindrical coordinates
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Explanation of all "its linearly independent derivatives"
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Question about solving linear first order non-homogeneous ODEs
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Using v substitution for first order homogenous DE and constraining solution
  • · Replies 4 ·
Replies
4
Views
2K
MHB Is This ODE Solvable by Substitution?
  • · Replies 3 ·
Replies
3
Views
2K
Finding area of ellipse using line integral.
  • · Replies 2 ·
Replies
2
Views
10K
Undergrad Where did this substitution technique go wrong?
  • · Replies 27 ·
Replies
27
Views
3K