Solution to a Polynomial Differential Equation

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So I'm having trouble find the exact solution to the following differential equation. [; \frac{dy}{dt} = \frac{1}{(y 2)^2} ;]

Separating variables and integrating we get

[ ;\int(y 2)² dy = \int dt \ \implies \frac{1}{3}y³ 2y² 4y = t c ; ]

At this point I don't understand the proper way to find the solution as a function of t. Normally I'd solve for y in terns of t but I'm not sure how to proceed here.

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Posted: 11 years ago
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