Given the following differential equation:(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \frac{dy}{dx}=\frac{\sigma y(\alpha x^{\alpha-1}y^{\beta}-\delta-\rho)}{x^\alpha y^\beta-\delta x-y}

[/itex]

and starting condition x(0)=x_{0}(=3, for instance)

and these parameters [itex] \alpha = 0.2; \beta = 0.1; \rho = 0.014; \delta = 0.05; b = 0.5; \sigma = 0.5; [/itex]

I want to find an exact solution. What I have tried so far is using the Mathematica tool DSolve, but when executed, Mathematica kept running for over 20 minutes without giving an answer.

I don't see any smart substitution or a way to make seperation of variables possible. Do you see any? I'm not asking for a complete solution or anything, but if you know a good book or manual where I can learn how to solve this, that's fine too.

Thanks!

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# Single ODE exact solution

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