Math 141 - Week 9 Notes Monday, March 15, 1999
Topics for this week -
- Separable differential equations
- Direction Fields
- Homogeneous differential equations
- Orthogonal Trajectories
- First-order linear differential equations
- Electric Circuits
- Exact equations
- Integrating factors
Covers: sections 15.1,15.2,15.3,15.4
Topics for next week -
- Complex numbers
- second-order linear equations
- nonhomogeneous linear equations
- Applications of second-order differential equations
- Series solutions
Covers: Appedix H, sections 15.5,15.6,15.7,15.8.
Examples
- Solve the differential equation
dy/dx=(y^{2}-x^{2})/2xy.
- Sketch the direction field of y'=y-x
- Find the orthogonal trajectories of a family of curves
y=kx^{2}, where k is an arbitary constant.
- Solve the initial value problem (1+x^{2})y'+2xy=3 sqrt(x),
where y(0)=2.
- applications to electric circuits
- Solve y-e^{x}cos(y)+(x+e^{x}sin(y))y'=0.
- Solve the initial value problem
3xy+2y^{2}+(x^{2}+2xy)y'=0 and y(1)=2.
- Solve
y-6x^{2}y^{3}+(2x-8x^{3}y^{2})y'=0.
nineth Homework Assignment - due on FRIDAY, March
26.
- Reading: In Chapter 15, read sections 15.1,15.2,15.3,15.4.
Appedix H
- 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:
- Section 15.1, p.975, #4,8, all of 11-14, 24(Maple!),36,40,44.
- Section 15.2, p.981, #8,14,20,29,30.
- Section 15.3, p.986, #4,10,16,20,24.
- Section 15.4, p.988, #8,12,20,25.