Question

The general solution of the differential equation \[ (2xy+y^2)\,dy=(x^2-y^2)\,dx \] is:

• A. \[ x^3-3x^2y-y^3=c \]
• B. \[ x^3-3x^2y+y^3=c \]
• C. \[ x^3-3xy^2+y^3=c \]
• D. \[ x^3-3xy^2-y^3=c \]

Hint:

For homogeneous differential equations, always check whether every term has the same degree. If yes, the substitution \(y=vx\) is usually the fastest and most reliable approach.

Answer 1

The Correct Option is D