SUNY Geneseo Department of Mathematics

First Order Linear Differential Equations

Tuesday, March 10

Math 222 01
Spring 2015
Prof. Doug Baldwin

Misc
- Exams will probably be graded after break
- Guest lecture by Prof. Macula
  - Extra credit for “homework”
  - See lecture summary for background
Questions?
- Slope fields?
  - Plot of solution slopes from differential equation
First Order Linear Differential Equations
- Sections 9.1 and 9.2
  - Euler’s method = solve differential equation numerically
  - First Order Linear differential equation
    - Standard form: dy/dx + P(x)y = Q(x)
    - e.g., dy/dx - ky = 0
      - P(x) = -k, Q(x) = 0
    - Put x dy/dx = x² + 3y in standard form?
      - x dy/dx - 3y = x²
      - dy/dx - 3y/x = x
      - Standard form! P(x) = -3/x, Q(x) = x
  - Solution strategy
    - Find v(x) such that v(x)( dy/dx + P(x)y ) = d/dx ( v(x) y )
    - Multiply both sides of standard form by v(x)
      - v(x)( dy/dx + P(x)y ) = v(x) Q(x)
    - Integrate to get
      - v(x) y = f(x)
    - So
      - y = f(x) / v(x)
    - v(x) = e raised to integral of P(x)
- Book example: dy/dx - 3y/x = x
- Problem set
Next
- RL circuit example from book
- Review “RL Circuits” part of section 9.2