Question

The solution of the differential equation \( y^2 dx + (x^2 - xy + y^2) dy = 0 \) is

• A. \( \tan^{-1}\left(\frac{x}{y}\right) + \ln y + C = 0 \)
• B. \( 2 \tan^{-1}\left(\frac{x}{y}\right) + \ln x + C = 0 \)
• C. \( \ln(v + \sqrt{x^2 + y^2}) + \ln y + C = 0 \)
• D. \( \ln(x + \sqrt{x^2 + y^2}) + C = 0 \)

Hint:

When solving a differential equation using substitution, make sure to fully simplify and separate the variables before performing integration.