NDA2015MathematicsDifferential EquationsActual
The solution of d y d x = 1-x^2-y^2+x^2 y^2 is where c is an arbitrary constant.
Options
- A⁻¹ y = ⁻¹ x + c
- B2 ⁻¹ y= 1-x^2 + ⁻¹ x+c
- C2 ⁻¹ y=x 1-x^2 + ⁻¹ x+c
- D2 ⁻¹ y=x 1-x^2 + ⁻¹ x+c
Correct answer
C. 2 ⁻¹ y=x 1-x^2 + ⁻¹ x+c
Step-by-step solution
aligned & d y d x = 1-x^2-y^2+x^2 y^2 & d y d x = (1-x^2 ) (1-y^2 ) & d y 1-y^2 = 1-x^2 d x & = d y 1-y^2 = 1-x^2 d x [integrating b/s] & = ⁻¹ ( y 1 )= x 2 1-x^2 + 1 2 ⁻¹ ( x 1 )+c & =2 ⁻¹ y=x 1-x^2 + ⁻¹ x+c aligned