COMEDK2024Morning ShiftMathematicsDifferential EquationsActual
The particular solution of d y d x + 1-y^2 1-x^2 =0 , when x=0, y= 1 2 is
Options
- A⁻¹ x+ ⁻¹ y= 2
- B⁻¹ x+ ⁻¹ y= 3
- C⁻¹ x- ⁻¹ y= 2
- D⁻¹ x+ ⁻¹ y= 6
Correct answer
D. ⁻¹ x+ ⁻¹ y= 6
Step-by-step solution
The given differential equation is dy dx + 1-y^2 1-x^2 = 0 . Separating the variables, we have dy 1-y^2 = - dx 1-x^2 . Integrating both sides, we get dy 1-y^2 = - dx 1-x^2 . This yields ⁻¹ y = - ⁻¹ x + C , which simplifies to ⁻¹ x + ⁻¹ y = C . Given the initial condition x=0 and y= 1 2 , we substitute these values into the equation: ⁻¹(0) + ⁻¹ ( 1 2 ) = C . 0 + 6 = C , so C = 6 . Therefore, the particular solution is ⁻¹ x + ⁻¹ y = 6 . Answer: ⁻¹ x+ ⁻¹ y= 6