Question

The general solution of the differential equation \[ x^{3}\,dx-xy^{2}\,dy+y^{3}\,dx=0 \] is

• A. \(y^{3}=3x^{4}+cx\)
• B. \(y^{3}=x^{3}\log|x|+c\)
• C. \(e^{\left(\frac{y^{3}}{x^{3}}\right)}=cx^{3}\)
• D. \(y^{3}=\log(cx)^{3}\)

Hint:

If the differential equation can be written in terms of \[ \frac{y}{x}, \] use the substitution \[ \boxed{y=vx.} \] This converts the equation into a separable differential equation.

Answer 1

The Correct Option is C