I'm taking my first ODE course, and I'm unsure what is meant in this question when it asks "Solve the following differential equation" (I have a list of DEs to solve). Some of them are really messy and I can't figure out an implicit solution. Would an explicit solution be acceptable?(adsbygoogle = window.adsbygoogle || []).push({});

Example:

[itex]\frac{dy}{dx} = \frac{x}{x^2y+y^3}[/itex]

Since this isn't an exact equation, I transform it and find the integrating factor

[itex]\frac{dy}{dx}(x^2y+y^3) - x = 0 [/itex]

and setting the partials [itex]\frac{∂}{∂x}N(x,y)μ(x) = \frac{∂}{∂y}M(x,y)μ(x) [/itex]

I get [itex]μ(x) = \frac{1}{x^2+y^2}[/itex]

I thought the integrating factor was supposed to be only a function of x, I may have made a mistake there.

Then I take [itex] \frac{∂}{∂y}\int M(x,y)μ(x) dx [/itex]

and I find [itex]f(x,y)=C=\frac{x^2+y^2}{2} - ln(x^2+y^2)[/itex]

This just doesn't look right, I feel like I'm using the wrong method. Can someone clear this up for me please?

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# Homework Help: Solutions to Differential equations

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