Math 141 - Week 9 Notes Monday, March 15, 1999

Topics for this week -

  1. Separable differential equations
  2. Direction Fields
  3. Homogeneous differential equations
  4. Orthogonal Trajectories
  5. First-order linear differential equations
  6. Electric Circuits
  7. Exact equations
  8. Integrating factors
  • Covers: sections 15.1,15.2,15.3,15.4
  • Topics for next week -

    1. Complex numbers
    2. second-order linear equations
    3. nonhomogeneous linear equations
    4. Applications of second-order differential equations
    5. Series solutions
  • Covers: Appedix H, sections 15.5,15.6,15.7,15.8.

  • Examples

    1. Solve the differential equation dy/dx=(y2-x2)/2xy.
    2. Sketch the direction field of y'=y-x
    3. Find the orthogonal trajectories of a family of curves y=kx2, where k is an arbitary constant.
    4. Solve the initial value problem (1+x2)y'+2xy=3 sqrt(x), where y(0)=2.
    5. applications to electric circuits
    6. Solve y-excos(y)+(x+exsin(y))y'=0.
    7. Solve the initial value problem 3xy+2y2+(x2+2xy)y'=0 and y(1)=2.
    8. Solve y-6x2y3+(2x-8x3y2)y'=0.



    nineth Homework Assignment - due on FRIDAY, March 26.
    1. Reading: In Chapter 15, read sections 15.1,15.2,15.3,15.4. Appedix H
    2. Make sure you can do all of the Core problems for sections 15.1 to 15.4. But write up only the following to be handed in: