COMEDK2023MathematicsDifferential Equations
The general solution of ( d y d x )^2=1-x^2-y^2+x^2 y^2 is
Options
- A2 ⁻¹ y=x 1-x^2 + ⁻¹ x+C
- B⁻¹ y=x ⁻¹ x
- C⁻¹ y= 1 2 ⁻¹ x+C
- D2 ⁻¹ y=x 1-y^2 +C
Correct answer
A. 2 ⁻¹ y=x 1-x^2 + ⁻¹ x+C
Step-by-step solution
aligned & Given, ( d y d x )^2=1-x^2-y^2+x^2 y^2 & ( d y d x )^2= (1-y^2 )-x^2 (1-y^2 )= (1-x^2 ) (1-y^2 ) & d y d x = (1-x^2 ) (1-y^2 ) & d y 1-y^2 = 1-x^2 d x aligned On integrating both sides, we get aligned & d y 1-y^2 = 1-x^2 d x & ⁻¹ y= x 2 1-x^2 + 1 2 ⁻¹ x+ C 2 & 2 ⁻¹ y=x 1-x^2 + ⁻¹ x+C aligned