Mathematics

Problem

A function

y=y(x)

satisfies

\displaystyle \frac{dy}{dx}=\dfrac{y^{2}-4}{x^{2}+x}

with the initial condition

y(1)=0

. Which of the following implicit equations represents the particular solution? a)

\displaystyle \ln\left|\frac{y-2}{y+2}\right|=\ln\left|\frac{2x}{x+1}\right|

\displaystyle \frac14\ln\left|\frac{y-2}{y+2}\right|=\ln\left|\frac{x}{x+1}\right|

\displaystyle \frac14\ln\left|\frac{y-2}{y+2}\right|=\ln\left|\frac{2x}{x+1}\right|

\displaystyle \frac14\ln\left|\frac{y+2}{y-2}\right|=\ln\left|\frac{2x}{x+1}\right|