MATH 046 Lecture Notes - Lecture 8: Integrating Factor, Product Rule, Lincoln Near-Earth Asteroid Research
Document Summary
Today we derive the formula for the solution of. + p(x)y = q(x) y (1) the general formula (2) some examples (3) initial value problems (4) bernoulli equation. We will show that the general solution is. From the chain rule, we get y = Multiplying the integrating factor to our equation, we get. = e (cid:2) p((cid:2) p) = p. which is the same as. Let(cid:1) us(cid:1) apply(cid:1) the(cid:1) formula(cid:1) directly(cid:1) to(cid:1) solve(cid:1) linear(cid:1) equation. For this equation, p = 2x and q = 2x and the integrating factor is. According to the formula, the general solution is. For this equation, p = 1 x and q = 3x. = e (cid:2) 1 x = e ln x = x. According to the formula, the general solution is y = + 2xy = 2x. y(0) = 3. From example 1, we know that the general solution is y = 1 + ce.
