COMEDK2022MathematicsDifferential Equations
The solution of the differential equation d y d x + 1-y^2 1-x^2 =0 is
Options
- A⁻¹ x+ ⁻¹ y=c
- B⁻¹ x+ ⁻¹ y=c
- C⁻¹ x+ ⁻¹ y=c
- D⁻¹ x+ ⁻¹ y=c
Correct answer
B. ⁻¹ x+ ⁻¹ y=c
Step-by-step solution
The given differential equation is dy dx + 1-y^2 1-x^2 = 0 . Separating the variables, we get dy 1-y^2 = - dx 1-x^2 . Integrating both sides, we have dy 1-y^2 = - dx 1-x^2 . Using the standard integral dt 1-t^2 = ⁻¹ t + C , we obtain ⁻¹ y = - ⁻¹ x + C . Rearranging the terms, we get ⁻¹ x + ⁻¹ y = C . Answer: ⁻¹ x+ ⁻¹ y=c