NDA2012MathematicsDifferential EquationsActual
What is the general solution of the differential equation x^2 d y+y^2 d x=0 ?
Options
- Ax+y=c
- Bx y=c
- Cc(x+y)=x y
- DNone of the above where c is the constant of integration
Correct answer
C. c(x+y)=x y
Step-by-step solution
aligned & x^2 d y+y^2 d x=0 & x^2 d y=-y^2 d x aligned d x x^2 + d y y^2 =0 on integrating, we get - 1 x - 1 y = C ₁ where C ₁ is constant of integration aligned x+y x y & =- C ₁ x+y & =- C ₁(x y) aligned 1 - C ₁ (x+y)=x y C (x+y)=x y where C = 1 - C ₁