<p>Find the general solution of the differential equation $\frac{\mathrm{d}m}{\mathrm{d}v}=\frac{{{m}^{2}}+m+1}{m+1}$.</p><p style="text-align: right;">[5]</p>

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

Differential Equations - General

Differential Equations

International Baccalaureate Higher Level Mathematics

IB HL Math

2019 ACJC Promo Q3

$\displaystyle\displaystyle\int \frac{m+1}{m^2+m+1} \, dm = \displaystyle\displaystyle\int 1 \, dv$

$\displaystyle\displaystyle\int \frac{A(2m+1) + B}{m^2+m+1} \, dm = v + C$

$\frac{1}{2}\displaystyle\displaystyle\int \frac{2m+1}{m^2+m+1} \, dm + \frac{1}{2}\displaystyle\displaystyle\int \frac{1}{(m+\frac{1}{2})^2 + \frac{3}{4}} \, dm = v + C$

$\frac{1}{2}\ln|m^2+m+1| + \frac{1}{2} \cdot \frac{\tan^{-1}\left(\frac{m+\frac{1}{2}}{\sqrt{\frac{3}{4}}}\right)}{\sqrt{\frac{3}{4}}} = v + C$

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

2019 ACJC Promo Q3

2019 ACJC Promo Q3

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