(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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: 3x^{2}y+8xy^{2}+[itex]([/itex]x^{3}+8x^{2}y+12y^{2}[itex])[/itex][itex]dy/dx[/itex]=0 Parameters: y(2)=1

2. Relevant equations

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

3. 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+8y^{2}-(24y+8x^{2}))/(3x^{2}y+8xy^{2}).

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 dont see it. Thank you

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# Homework Help: Can’t get a start on solving a first order differential equation

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