0주: 환영(Welcome)
W0.1 강좌 예고(Course Trailer)
W0.2~5 강좌 개요(Course Overview)
W0.6~7/1강 미분 방정식 소개 및 연습문제
(Introduction to Differential Equations & Practice Quiz)
1주: 1차 미분 방정식(Frst-order Differential Equation)
W1.1/2강 수치해석:오일러 방법(Euler Method)
W1.2/3강 1차 미분 방정식 세우기(Separable First-order equations)
W1.3/4강 1차 미분 방정식 세우기 예제(Separable First-order equations:Example)
W1.4 연습문제(Practice Quiz:Separable First-order ODEs)
W1.5/5강 선형 1차 미분 방정식(Linear First-order Equations)/동영상/영문자막
Meaning "Linear" in the y-variable.
- We have (dy/dx) is now multiplied anywhere, but its not multiplied by y.
- We have a 'y' multiplied by any function of x.
- Then we have just a function of x on the right-hand side.
The standard form of linear first-order ODE.
May NOT be separable.
If you pull the (p(x)y) term on the right-hand side, you may not be able to factor out the y and separate it.
Some first-order linear ODEs are separable but the general one is not. Luckily, there's analytical method to solve all linear first-order ODEs.
"The idea" is multiply it by something that's called an integrating factor.
Multiply by integrating factor μ(x), function of x, to both sides of 'Standard-form' by μ(x), we can find solution of standard ODE by direct integration.
How we can find μ(x)?
It's separable ODE,
[연습]----------------------------------------------------------
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