Problem with first-order nonlinear ordinary differential equation

[bobey]

i have problem to find the solution for : (3x³y+2xy+y³)+(x²+y²)dy/dx=0

i have tried the exact equation method :

(3x³y+2xy+y³)dx+(x²+y²)dy=0

thus M(x,y)=(3x³y+2xy+y³)

and N(x,y)= (x²+y²)

then deltaM/deltay=3x³+2x+3y²
and deltaN/deltax=2x

Since deltaM/deltay does not equal to deltaN/deltax, this imply that the equation is not exact

thus, finding/searching for integrating factor :

1. 1/N(deltaM/deltay-deltaN/deltax)=(3x³+3y³)/(3x³y+2xy+y³)

y cannot be eliminated . thus, this is a function of both x and y, not just x

2. 1/M(deltaN/deltax-deltaM/deltay)=(3x³+3y²)/(x²+y²)

x cannot be eliminated . thus, this is a function of both x and y, not just y


thus i cannot find the integrating factor in order to solve the DE. where I'm gone wrong? can somebody point it out? i guess may be in algebra...

 

[kosovtsov]

You are on right direction. But not all of ODEs have an easy integrating factor.

 

[bobey]

is there anyway for me to solve the de? please help me...