Question

I have a question regarding differential equations: why is there a y in u(t) dy/dt + u'(t)y= u(t) g(t)
link: http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx
equation number 4

Answer 1

because at the beginning they started with
dy/ddt + p(t)y=g(y)

Answer 2

dy/dt*

Answer 3

and it says that u(t)p(t)= u'(t)
which means they only substituted the u'(t) instead of p(t)u(t) so the y doesnt change

Answer 4

can u explain it frm d beginning

Answer 5

so the y is there since the beginning?

Answer 6

what