COMEDK2023Morning ShiftMathematicsDifferential EquationsActual
The general solution of ( d y d x )^2=1-x^2-y^2+x^2 y^2 is
Options
- A⁻¹ y= 1 2 ⁻¹ x+C
- B2 ⁻¹ y=x 1-x^2 + ⁻¹ x+C
- C⁻¹ y=x ⁻¹ x
- D2 ⁻¹ y=x 1-y^2 +C
Correct answer
B. 2 ⁻¹ y=x 1-x^2 + ⁻¹ x+C
Step-by-step solution
( dy dx )^2 = (1-x^2)(1-y^2) Separating variables: dy 1-y^2 = 1-x^2 dx Integrating both sides: ⁻¹y = x 2 1-x^2 + 1 2 ⁻¹x + C₁ Multiplying by 2: 2 ⁻¹y = x 1-x^2 + ⁻¹x + C