NOTES FOR CALC III SHAUMS OUTLINE

1
NOTES FOR CALC IIISHAUMS OUTLINE

• CHAPTER 5
• LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS

2
Solving
Note All of y, p, q and m will be functions of x.
We will start with a simpler problem. Suppose we
had
Then we could solve
3
Step 2 Solving
From Step 1
Integrate both sides
Integrate the left side
The solution
4
Step 3 Solving
We would like to change
Into
This would require
And we have
5
Step 4 Solving
From Step 3 we have
and
Substituting
Subtract my and
if we cancel the y
Next step, solving for m
6
Step 5 Solving
From Step 4
Separate the variables
Integrate both sides
7
Step 6 Solving
From Step 5
We can integrate the left side
And if then we would
have a solution.
8
The Method for Solving

• Now we have a method of solution
• Put the equation in the form
• Set and solve for m
• Solve

9
The Method for Solving Bernoulli

• Now we have a method of solution
• Put the equation in the form
• Set and solve for
  m
• Solve

NOTE THIS METHOD ALSO SOLVES THE LINEAR CASE,
JUST SET n 0.
10
Example Solve

• Put the equation in the form
• Set and solve for m
• Solve

11
Check
12
END CHAPTER 5