Find the general solution of the differential equation $\frac{\mathrm{d}m}{\mathrm{d}v}=\frac{{{m}^{

Question

Find the general solution of the differential equation $\frac{\mathrm{d}m}{\mathrm{d}v}=\frac{{{m}^{2}}+m+1}{m+1}$. [5]

Accepted Answer

$\displaystyle\frac{1}{2}\ln|m^2+m+1| + \frac{1}{\sqrt{3}}\tan^{-1}\left(\frac{2m+1}{\sqrt{3}}\right) = v + C$

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