Session 5

Solution of First-Order Linear Equations

1. Mattuck video lecture 3 23:13 -- 42:50
   Solve standard first order: integrating factor
   Example $xy' - y = x^3$ 

2. Mattuck video lecture 3 42:50 -- 50:22
   CC system $T' + kT = kT_e$
   Definite integral soln to IVP

3. Doc 5.1
   Integrating factors

4. Doc 5.2
   radio quiz: intepret $k$.

5. Doc 5.3
   radio quiz: Suppose x(t) measures temp in degrees C. What are the units on k? dx/dt? q_e?

6. Recitation video
   Orloff rec 1, topic 2, sugg prob
   3. y'+2y=2
   4. y'+2y=e^{2t}
   7. y'+2y=2+5e^{2t}
   8. Show y'+y^2=q does not satisfy superposition

7. Doc 5.4
   Mattuck IR.4 discontinuous inputs use x'+kx=q

8. Haynes recit 4 problems

-----------
Haynes lec 4
1. Homogeneous eq --> x_h
2. Diffusion eq (cc DE)
   example
   3. Integrating factors
   4. IC
5. General integrating factor (for non cc)

-- Add in general solution x_p+cx_h
-- Add in continuation theory from notes ch 3

Haynes notes ch3
Var of params
Theory --continuation of solutions
--------
Mattuck IR.1
   y'+ky=q
   integrating factor
IR.3
	Temperature, physical inputs
IR.4
  Discontinuous inputs
IR.5
  Sinusoidal inputs