The solution of the differential equation $y\left({\sin }^{2}x\right)dy+\left(\sin x\cos x\right)y^{2}dx=xdx$ is (where $C$ is the constant of integration)

• A

  $\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}x\cdot y=x^2+C$
• Correct answer
  B

  $\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}x\cdot y^2=x^2+C$
• C

  $\mathrm{s}\mathrm{i}\mathrm{n}x\cdot y^2=x^2+C$
• D

  $\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}x\cdot y^2=x+C$

Hence, the correct answer is option: 'B'.