i have problem to find the solution for : (3x(adsbygoogle = window.adsbygoogle || []).push({}); ^{3}y+2xy+y^{3})+(x^{2}+y^{2})dy/dx=0

i have tried the exact equation method :

(3x^{3}y+2xy+y^{3})dx+(x^{2}+y^{2})dy=0

thus M(x,y)=(3x^{3}y+2xy+y^{3})

and N(x,y)= (x^{2}+y^{2})

then deltaM/deltay=3x^{3}+2x+3y^{2}

and deltaN/deltax=2x

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

thus, finding/searching for integrating factor :

1. 1/N(deltaM/deltay-deltaN/deltax)=(3x^{3}+3y^{3})/(3x^{3}y+2xy+y^{3})

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

2. 1/M(deltaN/deltax-deltaM/deltay)=(3x^{3}+3y^{2})/(x^{2}+y^{2})

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...

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# Problem with first-order nonlinear ordinary differential equation

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