Solve the differential equation: $x\dfrac{dy}{dx}=\dfrac{1}{y^3}$ Would anybody be able to help me work through this problem?
I am having some trouble with it. 
$$x\dfrac{dy}{dx}=\dfrac{1}{y^3}$$

From
$$x\dfrac{dy}{dx}=\dfrac{1}{y^3}$$
we have
$$\int y^3dy=\int\frac{dx}{x}$$
So
$$\frac{1}{4}y^4=\ln{|x|}+C\Rightarrow y=\pm\sqrt[4]{4\ln{|x|}+C}$$
You can find a specific solution from an initial condition.
