If a and b are arbitrary constants, then the differential equation corresponding to the family of curves $y=\tan (a x+b)$ is

• A

  $\left(1+x^2\right) y_2-2 y y_1+y=0$
• Correct answer
  B

  $\left(1+y^2\right) y_2-2 y y_1^2=0$
• C

  $\left(1+x^2\right) y_2+2 y y_1^2=0$
• D

  $\left(1+y^2\right) y_2-2 y y_1^2+y=0$

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