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AP EAMCET202316 May 2023Morning ShiftMathematicsDifferential EquationsActual

If _ x y(x)= 2 , then the solution of x^3 y d y d x =2 is y=

Options

  1. A3 x ^2
  2. B1 x
  3. C1 x^2
  4. D2 x^3

Correct answer

C. 1 x^2

Step-by-step solution

x^3 y d y d x =2 y d y= 2 x^3 d x Integrating both sides, we get y d y=2 1 x^3 d x - y=2 x⁻² -2 +C y= 1 x^2 -C ...(i) Taking _ x on both sides : aligned & _ x y= _ x 1 x^2 -C & ( _ x y )=0-C ( 2 )=-C C=0 aligned Putting the value of C in equation (i), we get : y= 1 x^2 -0 y= 1 x^2

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