COMEDK2018MathematicsIndefinite Integration
-The solution of the differential equation d y d x =(x+y)² is
Options
- A1 x+y =c
- B⁻¹(x+y)=x+c
- C⁻¹(x+y)=c
- D⁻¹(x+y)=x+c
Correct answer
D. ⁻¹(x+y)=x+c
Step-by-step solution
We have, d y d x =(x+y)² Let x+y=z d y d x +1= d z d x d y d x = d z d x -1 Now, given equation becomes d z d x -1=z² d z d x =1+z² d x= d z 1+z² On integrating both sides, we get array ll & d x= d z 1+z² & c+x= ⁻¹(z) & ⁻¹ z=x+c & ⁻¹(x+y)=x+c array