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NDA2015MathematicsDifferential EquationsActual

What is the solution of the differential equation d x d y + x y -y^2=0 ? where c is an arbitrary constant.

Options

  1. Ax y=x^4+c
  2. Bx y=y^4+c
  3. C4 x y=y^4+c
  4. D3 x y=y^3+c

Correct answer

C. 4 x y=y^4+c

Step-by-step solution

aligned & d x d y + x y -y^2=0 & d x d y + x y =y^2 aligned This is a linear differential equation of the form dx dy + P ₁ x = Q ₁ Here, P = 1 y and Q = y ^2 I.F. = e ^ P d y = e ^ 1 y d y = e ^ y =y So, required solution is aligned & x y= y^2 y d y+c & x y= y^3 d y+c & x y= y^4 4 +c & 4 x y=y^4+c aligned Option (C) is correct.

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