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

1. May 25, 2012

### ifly2hi

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: 3x2y+8xy2+$($x3+8x2y+12y2$)$$dy/dx$=0 Parameters: y(2)=1

2. Relevant equations
$∂M/∂y$=$∂N/∂x$ (Exactness) & $(My-Nx)/N$ (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+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 dont see it. Thank you

Last edited by a moderator: May 25, 2012
2. May 25, 2012

### cjc0117

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

Last edited: May 25, 2012
3. May 25, 2012

### HallsofIvy

Staff Emeritus
6xy+ 8y is My but 24y+ 8x2 is Ny, not Nx.