# 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.