Question

Solution of the differential equation
$\left[3 x y^{2}+x \sin (x y)\right] d y+\left[y^{3}+y \sin (x y)\right] d x=0$ is

• A. $x y^{3}-\cos x y=c$
• B. $x y^{3}+\cos x y=c$
• C. $x y^{2}-\cos x y=c$
• D. $x y^{2}+\sin x y=c$

Answer 1

Answer: (A)

$3 x y^{2} d y+y^{3} d x+\sin (x y)(x d y+y d x)=0$
or $d\left(x y^{3}\right)+\sin (x y) d(x y)=0$
On integrating, we get
$x y^{3}-\cos x y=c$