Question

The general solution of the differential equation $x \, dy - y \, dx = y^2 \, dx$ is:

• A. $y = \frac{x}{C - x}$
• B. $x = \frac{2y}{C + x}$
• C. $y = (C + x)(2x)$
• D. $y = \frac{2x}{C + x}$
• E. $x = \frac{y}{C - x}$

Hint:

When you see $x \, dy - y \, dx$, try dividing by $y^2$ to get $-d(x/y)$ or by $x^2$ to get $d(y/x)$. Here, dividing by $y^2$ gives $d(x/y) = -dx/x$ if rearranged slightly, which is even faster.

Answer 1

The Correct Option is A