KCET2011MathematicsDifferential Equations
The general solution of ( d y d x )²=1-x²-y²+x² y² is
Options
- A2 ⁻¹ y=x 1-x² + ⁻¹ x+C
- B⁻¹ y=x ⁻¹ x+C
- C⁻¹ y= 1 2 ⁻¹ x+C
- D2 ⁻¹ y=x 1-y² +C
Correct answer
A. 2 ⁻¹ y=x 1-x² + ⁻¹ x+C
Step-by-step solution
Given, ( d y d x )²=1-x²-y²+x² y² ( d y d x )²= (1-x² )-y² (1-x² ) d y d x = (1-x² ) (1-y² ) d y (1-y² ) = (1-x² ) d x (on integrating) ⁻¹ y= x 2 1-x² + 1 2 ⁻¹ x+ C 2 2 ⁻¹ y=x 1-x² + ⁻¹ x+C