Integrating Factors

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Integrating Factors

Definition: Integrating Factor

If the equation M(x,y)dx+N(x,y)dy=0 is not exact, but the equation μ(x,y)M(x,y)dx+μ(x,y)N(x,y)dy=0 for μ(x,y)0 is exact, then the function μ(x,y) is an integrating factor of the equation.

Investigation 01

Determine if the following μ equations are integrating factors of the DEs. Explain.

  1. Is μ(x)=x an integrating factor of (3x2+y)dx+(2x2yx)dy=0

  2. Is μ(x)=1x2 an integrating factor of (3xy+y2)dx+(x2+xy)dy=0

  3. Is μ(y)=1y4 an integrating factor of (2y7+y4)dx+(6xy63)dy=0

  4. Is μ(x,y)=1x5y2 an integrating factor of (x3y2y2)dx+x4dy=0

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Last Modified: Monday, 6 September 2020 13:33 EDT