Question

The solution of $y^{4}dx + 2xy^{3}dy = \frac{ydx - xdy}{x^{3}y^{3}}$ is}

• A. $xy^{3} + 3 \ln(\frac{y}{x}) = \text{constant}$
• B. $x^{3}y^{6} + 3 \ln(\frac{y}{x}) = \text{constant}$
• C. $x^{3}y^{6} - 3 \ln(\frac{y}{x}) = \text{constant}$
• D. $x^{6}y^{3} + 3 \ln(\frac{y}{x}) = \text{constant}$

Hint:

Look for the pattern $d(x^n y^m) = n x^{n-1} y^m dx + m x^n y^{m-1} dy$ to solve complex product differentials.

Answer 1

The Correct Option is B