COMEDK2014MathematicsIndefinite Integration
The solution of (x+y)² (x d y d x +y )=x y (1+ d y d x ) is
Options
- A(x y)=- 1 x+y +C
- B( x y )=- 1 x+y +C
- C(x y)= 1 x-y +C
- DNone of the above
Correct answer
A. (x y)=- 1 x+y +C
Step-by-step solution
Given, differential equation is aligned & (x y)⁻¹ (x d y d x +y )=(x+y)⁻² (1+ d y d x ) & (x y)⁻¹ (x d y d x +y ) d x= (x+y)⁻² (1+ d y d x ) d x ( i ) aligned Using integral, (f(x))^ n f^ (x) d x= .(f(x))^ n+1 ) n+1 and array ll From Eq. (i) & (x y)= (x+y)⁻¹ -1 +C & (x y)= -1 x+y +C array