The question I have is with the DE (x^2 4y)dx (4x - 4y^2)dy = 0. I know M=x^2 4y

Question

The question I have is with the DE (x^2 4y)dx (4x - 4y^2)dy = 0.
I know M=x^2 4y and N= 4x-4y^2.
(*note: i will use pd for partial differentiation and S for integral)
They are exact as pd(M)/pd(y) = 4 and pd(N)/pd(x) = 4
I set pd(g)/pd(x) = M and pd(g)/pd(y)=N
then i did
S x^2 4y h(y) which resulted in
(x^3)/3 4xy h(y)
then I did pd(g)/pd(y) = 0 4x h'(y)
= 4x h'(y)
then
4x h'(y) = 4x - 4y^2
h'(y) = -4y^2
*then took the integral
h(y) = -(4y^3)/3 C
and I got the function (x^3)/3 4xy - (4y^3)/3 C = C
finally getting (x^3)/3 4xy - (4y^3)/3 = C as the solution to the given equation
Did i do something wrong or is it possibly that I inputted the answer wrong?
They ask for the answer as F(x,y), but i just used g(x,y) when working it out

Explanation / Answer

you will find answer in this below given site and it is helpful to you and many model problems are there for you to practise http://samples.jbpub.com/9780763779665/79665_CH03_PASS02.pdf

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