COMEDK2018MathematicsIndefinite Integration
The particular solution of y x d y d x = 1+y² 1+x² , when x=1, y=2 is
Options
- A5 (1+y² )=2 (1+x² )
- B2 (1+y² )=5 (1+x² )
- C5 (1+y² )= (1+x² )
- D(1+y² )=2 (1+x² )
Correct answer
B. 2 (1+y² )=5 (1+x² )
Step-by-step solution
We have, y x d y d x = 1+y² 1+x² aligned & y d y 1+y² = x d x 1+x² & 2 y d y 1+y² = 2 x d x 1+x² aligned Integrating both sides, we get 2 y d y 1+y² = 2 x d x 1+x² array r (1+y² )= (1+x² )+ c 1+y²=c (1+x² ) array Now, y=2 at x=1 So, 5=c(2) 2 c=5 Therefore, 2 (1+y² )=5 (1+x² )