Additional Topics on the Equations of Order One

Integrating Factors Found by Inspection

The following are the four exact differentials that occurs frequently.

  1. $d(xy) = x \, dy + y \, dx$
     
  2. $d\left( \dfrac{x}{y} \right) = \dfrac{y \, dx - x \, dy}{y^2}$
     
  3. $d\left( \dfrac{y}{x} \right) = \dfrac{x \, dy - y \, dx}{x^2}$
     
  4. $d\left( \arctan \dfrac{y}{x} \right) = \dfrac{x \, dy - y \, dx}{x^2 + y^2}$
  5.  

  6. $d\left( \arctan \dfrac{x}{y} \right) = \dfrac{y \, dx - x \, dy}{x^2 + y^2}$

 

02 - Solution to Radical Equations Jhun Vert Fri, 04/17/2020 - 02:00 pm

Determine the value of $x$ from the following equations:

  1. $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$
     
  2. $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$