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AP EAMCET202022 Sep 2020Morning ShiftMathematicsDifferential EquationsActual

Solve the differential equation given below x d y d x =y+ x^2+y^2

Options

  1. Ax^2=c [y+ y^2+x^2 ]
  2. By^2=c [x+ y^2-x^2 ]
  3. Cy^2=c [x+ ⁻¹ ( 1+y^2 ) ]
  4. Dy^2=c [x- y^2+x^2 ]

Correct answer

A. x^2=c [y+ y^2+x^2 ]

Step-by-step solution

Given differential equation aligned x d y d x & =y+ x^2+y^2 d y d x & = y+ x^2+y^2 x aligned Now, put y=v x d y d x =v+x d v d x On doing substitution, we get aligned & v+x d v d x =v+ 1+v^2 & d v 1+v^2 = d x x & _ C+ _ ( 1+v^2 +v )= _ x & [ (y+ x^2+y^2 ) C ]=2 _ x & x^2=C [y+ y^2+x^2 ] aligned Hence, option (1) is correct.

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