Question

solue (xy²+ x) dx + (yx²+y)dy=0​

Answer 1

Well, I will follow through with the suggestion of the other solver.

I will multiply by x^m.y*n.

(x^my^(n+1)-x^(m+1)y^(n+2))dx + (x^(m+1)y^n+x*(m+2)y^(n+2)$dy = 0.

del M/del y = (n+1)x^m y^n-(n+2)x^(m+1)y^(n+1),

del N/del x= (m+1)x^my^n+(m+2)x^(m+1)y^(n+2).

I am wasting too much time on this. It does not seem to be working!

Maybe I have made some errors? I leave it to you. I’m off to bed.

Answer 2

Answer:

{x²+1} .{y²+1}  = K

Step-by-step explanation:

(xy²+ x) dx + (yx²+y)dy = 0​

(yx²+y )dy    =  -(xy²+ x)  dx

re-arranging x,y to make it variable separable

  x dx /(x²+1)  = - y dy/(y²+1)

2 x dx /(x²+1)  = - 2y dy/(y²+1)

integrating both sides

Ln{x²+1} =- Ln{y²+1) +C

Ln({x²+1} .{y²+1})   = C

{x²+1} .{y²+1}  = K    ( k is arbitrary Constant)  is general solution