- #1
KT KIM
- 24
- 0
I am studying ode now, and my text has that
If y'=f(y/x)
Then, setting y/x=u ; y=ux is a way to solve it.
I understand the idea, turn orignal form to separable form.
But I can't get the differentiation, Book says
y'=u'x+u by product rule which I already know.
Here my question is why u=y/x that obviously has two variables x & y, u(x,y) should be differentiated respect to x like it only has one variable x ( like u(x) )
If y'=f(y/x)
Then, setting y/x=u ; y=ux is a way to solve it.
I understand the idea, turn orignal form to separable form.
But I can't get the differentiation, Book says
y'=u'x+u by product rule which I already know.
Here my question is why u=y/x that obviously has two variables x & y, u(x,y) should be differentiated respect to x like it only has one variable x ( like u(x) )