Solve the homogeneous equation dy/dx = (ax + y)/(x - y)

1. A.
   $\tan^{-1}\!\left(\frac{y}{x}\right) + \log\sqrt{y^2+3x^2} \cdot x^{-2} = \log x + C$
2. B.
   $\frac{1}{\sqrt{3}}\tan^{-1}\!\left(\frac{y}{\sqrt{3}x}\right) + \log\left(\frac{\sqrt{y^2+3x^2}}{x}\right)^{1/2} = \log x + C$
3. C.
   $\frac{1}{\sqrt{3}}\tan^{-1}\!\left(\frac{y}{\sqrt{3}x}\right) - \log\left(\frac{\sqrt{y^2+3x^2}}{x}\right)^{1/2} = \log x + C$
4. D.
   $\tan^{-1}\!\left(\frac{x}{y}\right) + \log\sqrt{y^2+3x^2} \cdot x^{-2} = \log x + C$

Tap an option to check your answer.

1. A.
   $c(x^2 + y^2)^{\frac{1}{2}} + e^{\tan^{-1}\left(\frac{y^2}{x}\right)} = 0$, where c is an arbitrary constant
2. B.
   $c(x^2 + y^2)^{\frac{1}{2}} = e^{\tan^{-1}\left(\frac{y}{x}\right)}$, where c is an arbitrary constant
3. C.
   $c(x^2 - y^2) = e^{\tan^{-1}\left(\frac{y}{x}\right)}$, where c is an arbitrary constant
4. D.
   $c(x^2 + y^2) = e^{\tan^{-1}\left(\frac{y}{x}\right)}$, where c is an arbitrary constant

Tap an option to check your answer.