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ifly2hi
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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+[itex]([/itex]x3+8x2y+12y2[itex])[/itex][itex]dy/dx[/itex]=0 Parameters: y(2)=1
Homework Equations
[itex]∂M/∂y[/itex]=[itex]∂N/∂x[/itex] (Exactness) & [itex](My-Nx)/N[/itex] (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
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