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BITSAT2014MathematicsDifferential EquationsActual

Solution of differential equation x²=1+ ( x y )⁻¹ d y d x + ( x y )⁻² ( d y d x )² 2 ! + ( x y )⁻³ ( d y d x )³ 3 ! + is

Options

  1. Ay²=x² ( x²-1 )+C
  2. By=x²( x-1)+C
  3. Cy²=x( x-1)+ C
  4. Dy=x² e^ x² + C

Correct answer

A. y²=x² ( x²-1 )+C

Step-by-step solution

x²=e^ ( x y )⁻¹ ( d y d x ) x²=e^ ( y x ) ( d y d x ) x²= y x d y d x or x x² d x= y d y Put x²=t 2 x d x=d t 1 2 t d t= y² 2 C+t t-t=y² or y²=x² ( x²-1 )+C

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