Question

Solution of differential equation $\left(2 x \cos y+y^{2} \cos x\right) d x+\left(2 y \sin x-x^{2} \sin y\right) d y=0$ is

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

Answer 1

Answer: (A)

$2 x \cos y \,d x+y^{2} \cos x \,d x+2 y \sin x \,d y-x^{2} \sin y \,d y=0$
$\Rightarrow \left(2 x \cos y\, d x-x^{2} \sin y \,d y\right)+$
$\quad\left(y^{2} \cos x d x+2 y \sin x \,d y\right)=0$
$\Rightarrow d\left(x^{2} \cos y+y^{2} \sin x\right)=0$
$\Rightarrow x^{2} \cos y+y^{2} \sin x=C$