AI Tutor
Back to Exact equations

Exercise 102

Avg difficulty 2.5

Find the integrating factor for the following equations making them into exact equations:

  1. 1y dx+3y dy=0\frac{1}{y}\, dx + 3y \, dy = 0
  2. dx−e−x−y dy=0dx - e^{-x-y} \, dy = 0
  3. (cos⁡(x)y2+1y) dx+xy2 dy=0\left( \frac{\cos(x)}{y^2} + \frac{1}{y} \right) \, dx + \frac{x}{y^2} \, dy = 0
  4. (2y+y2x) dx+(2y+x) dy=0\left( 2y + \frac{y^2}{x} \right) \, dx + ( 2y+x )\, dy = 0

Lebl, Notes on Diffy Qs, §1.8 Exact equations, exercise 102

AI Tutor

Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.