MAT244--2020F > Chapter 2

LEC5101 Question

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yingxuanwang:
Hi, I have a question when I solve the first order equation.
I have found that sometimes to multiple a factor to the equation to construct a exact equation is much more convenient to use formula to solve it. But it is hard for me to find such a integral factor, is there any techniques to use this method? Or how can I know when I should use such method?
Thanks.

Victor Ivrii:
You need to wait lectures ; there will be shown some recepies  to find integrating factors, but there is no general algorithm

RunboZhang:
I think a general idea behind integrating factor is the use of product rule. Since a general form is u(t)dy/dx +u(t)p(t)y = u(t)g(t), and we can observe a pattern of u'y+uy' on LHS. Thus the LHS becomes d(u(t)y)/dt, and it makes the equation easier to solve. More details are expanded in the textbook starting from P24 and those illustrations and examples are quite useful. I don't know if I have addressed your problem, if I did not make my point clear please comment below.

Victor Ivrii:
I believe question was not about Linear Equations but more general ones