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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Differential Equations

NDA 2020 · Mathematics · Differential Equations

The function u(x, y)=c which satisfies the differential equation...

The function u(x,y)=cu(x, y)=c which satisfies the differential equation x(dx−dy)+y(dy−dx)=0x(d x-d y)+y(d y-d x)=0, is

Options

  1. Ax2+y2=xy+cx^2+y^2=x y+c
  2. Bx2+y2=2xy+cx^2+y^2=2 x y+c
  3. Cx2−y2=xy+cx^2-y^2=x y+c
  4. Dx2−y2=2xy+cx^2-y^2=2 x y+c

Correct answer

B. x2+y2=2xy+cx^2+y^2=2 x y+c

Step-by-step solution

x(dx−dy)+y(dy−dx)=0x(d x-d y)+y(d y-d x)=0 On integrating both sides, we have ∫x(dx−dy)+∫y(dy−dx)=C( where C= constant )x22−xy+y22−xy=Cx2+y2−2xy=C Or, x2+y2=2xy+C\begin{aligned} & \int x(d x-d y)+\int y(d y-d x)=C(\text{ where } C=\text{ constant }) \\ & \frac{x^2}{2}-x y+\frac{y^2}{2}-x y=C \\ & x^2+y^2-2 x y=C \\ & \text{ Or, } x^2+y^2=2 x y+C \end{aligned}
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