1. I got a bit stuck on the second part of a question below, I'll show my first part working out as it's needed for the second part...

Q: The variables x and y are related by the differential equation i) Use the substitution y=xz, where z is a function of x, to obtain the differential equation For this I got:   So then part two says:

ii) Find by integration the general solution of the differential equation A.

I got this far on this question, and then got a bit stuck: I don't really know where to go from here... So any help would be appreciated! Thanks!  2.

3. you have like 80% finished the whole thing,      4. Hmmm... I did it and I got a solution slightly different to that: (following on from where I left off)   Hmmm...  5. it is really so difficult for me. but I indeed ger something from it  6. Originally Posted by Heinsbergrelatz
you have like 80% finished the whole thing,    You have left out the constant of integration: whence:  Originally Posted by x(x-y)
Hmmm... I did it and I got a solution slightly different to that: (following on from where I left off)   Hmmm...
You have simply got the solution in implicit form.

Set for simplicity, solve with respect to , and you get the above explicit solution.

The given equation, is of the general form: with being a Homogeneous Function of the th degree i.e. one satisfying: . In our case: , whence: , altogether a homogeneous function of the th degree.

It could also assume the form: , i.e. we could consider as the unknown function and as the independent variable: . This could be solved by solving the above implicit solution wrt . Namely:  . (A good exercise here would be to specify the domain of each of the four solutions given for by this formula!)  7. Please solve the following differential equation step by step:

(x^2 - 3y^2)xdx + (3x^2 - y^2)ydy = 0  