NDA2020MathematicsDifferential EquationsActual
The function u(x, y)=c which satisfies the differential equation x(d x-d y)+y(d y-d x)=0 , is
Options
- Ax^2+y^2=x y+c
- Bx^2+y^2=2 x y+c
- Cx^2-y^2=x y+c
- Dx^2-y^2=2 x y+c
Correct answer
B. x^2+y^2=2 x y+c
Step-by-step solution
x(d x-d y)+y(d y-d x)=0 On integrating both sides, we have aligned & x(d x-d y)+ y(d y-d x)=C( where C= constant ) & x^2 2 -x y+ y^2 2 -x y=C & x^2+y^2-2 x y=C & Or, x^2+y^2=2 x y+C aligned