KCET2022MathematicsDifferential Equations
The solution of the differential equation d y d x =(x+y)^2 is
Options
- A⁻¹(x+y)=x+C
- B⁻¹(x+y)=0
- C⁻¹(x+y)=C
- D⁻¹(x+y)=x+C
Correct answer
A. ⁻¹(x+y)=x+C
Step-by-step solution
d y d x =(x+y)^2 Let x+y=t 1+ d y d x = d t d x Eq. (i) can be written as gathered d t d x -1=t^2 d t d x =t^2+1 d t t^2+1 =d x gathered aligned & d t t^2+1 = d x ⁻¹ t=x+C & ⁻¹(x+y)=x+C aligned