Lecture 05 - Jan 14

First Order Linear DE (Continued)

is the soln of

Proof

Let be the solution. We are interested in finding a such that is integrable,

Given that is a function, where ,

Let

If , then is the soln of .

If , then is the particular soln of (I).

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Problems

Find all the solutions:

1.

2.

3.

Solution

Problem 2:

P = , Q =

Problem 3:

P = , Q =

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Bernoulli Equation

(⊕)

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Problem

Solve,

Solution

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Riccati Equation