Now make
someone please enlighten me on each step taken (as well as integrating both sides of the separable equation involving z and x) in solving the following equation:
(x^2)y'=7(y^2)-2xy
using the subsitution z=(y/x)
i know what has to be done, but im having troubles simplifying into a regular funtion y(x)...
this can be done using bernouilli's method but wanna get the same using the homogeneous substituion method
thanks
yea i did that, but solve down to the part where you end up with a separable equation dz/7(z^2)-3z = dx/x.
i tried integrating both sides, and especially the left one needed more tactics where i used partial integration {dz/7(z^2)-3z} = 1/7[A/z + B/{z-(3/7))]
my problem here is integrating and getting a solution y(x) after back substituting z=(y/x). I did the same ODE using bernouillis and i got
y(x)=-7x^(-1) +Cx^(-2). Just want to see how to reach the same results using the homogenous substitution technique
thanks in advance!