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How to make an unexact equation exact?
I understand that to make an equation exact, you need to apply an integrating factor. And there are 3 cases to find such integrating factor.
However, what if those 3 cases fail? How would you solve the problem?
For example: (2x-5y)dx + (4x - y)dy = 0
1 Answer
- Tabula RasaLv 61 decade agoFavorite Answer
I would solve it as a first-order homogeneous differential equation:
(2x-5y)dx + (4x - y)dy = 0
express dy/dx:
dy/dx = (5y - 2x)/(4x - y)
Divide top and bottom of the RHS by x≠0:
y ' = (5y/x - 2)/(4 - y/x)
This is the first order homogeneous equation.
Substitution y/x = u, y = ux, y ' = u ' x + u
u ' x + u = (5 u - 2)/ (4 - u)
I leave it to finish it to you.
Email me if you need more help.