General solution of the differential equation $\frac{2y\, dx-3x\, dy}{y}=0$ is
(c is an arbitrary constant)
Answer & explanation
Correct answer: option 3
$\frac{2ydx}{y}-\frac{3xdy}{y}=0⇒\frac{2ydx}{y}=\frac{3xdy}{y}$
$⇒\int\frac{2}{x}dx=\int\frac{3}{y}dy$ (integrating both sides)
$⇒2\log x=3\log y+\log c$
$⇒\log x^2=\log y^3c$
so $y^3c=x^2$
so $y^3=cx^2$