Can’t get a start on solving a first order differential equation

[ifly2hi]

Homework Statement

Am looking at a first order, non linear differential equation. I want to solve for a general solution and will have to find a constant with given parameters. Equation: 3x²y+8xy²+$($x³+8x²y+12y²$)$$dy/dx$=0 Parameters: y(2)=1

Homework Equations

$∂M/∂y$=$∂N/∂x$ (Exactness) & $(My-Nx)/N$ (integrating factors)

The Attempt at a Solution

I have tried to use separation of variable with no avail. When I try to separate them I can’t get it into terms of just x or just terms of y. I have tested for exactness and it failed, so I moved to the next step of integrating factors. After trying to solve for integrating factors I still cannot get function of x alone or y alone. When solveing for the equation listed in “Relevant equations” I get:((6xy+8y²-(24y+8x²))/(3x²y+8xy²).

Have tried intergrating factors both ways and still can't get a function of x or y alone. Can someone point in the right direction to starting this problem. I am swinging the bat but missing the ball b/c I don't see it. Thank you

 

[cjc0117]

You must have computed $M_{y}$ and/or $N_{x}$ incorrectly, because they are equal.

 

[HallsofIvy]

Homework Statement

Am looking at a first order, non linear differential equation. I want to solve for a general solution and will have to find a constant with given parameters. Equation: 3x²y+8xy²+$($x³+8x²y+12y²$)$$dy/dx$=0 Parameters: y(2)=1

Homework Equations

$∂M/∂y$=$∂N/∂x$ (Exactness) & $(My-Nx)/N$ (integrating factors)

The Attempt at a Solution

I have tried to use separation of variable with no avail. When I try to separate them I can’t get it into terms of just x or just terms of y. I have tested for exactness and it failed, so I moved to the next step of integrating factors. After trying to solve for integrating factors I still cannot get function of x alone or y alone. When solveing for the equation listed in “Relevant equations” I get:((6xy+8y²-(24y+8x²))/(3x²y+8xy²).

6xy+ 8y is M_y but 24y+ 8x² is N_y, not N_x.

Have tried intergrating factors both ways and still can't get a function of x or y alone. Can someone point in the right direction to starting this problem. I am swinging the bat but missing the ball b/c I don't see it. Thank you