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MHT CET202122 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

Solution of the differential equation y^ = (x^2+y^2 ) x y , where y(1)=-2 is given by

Options

  1. Ay^2=4 x^2 x^2+x^2
  2. By^2=x^2 x-x^2
  3. Cy^2=x x^2+4 x^2
  4. Dy^2=x^2 x^2+4 x^2

Correct answer

D. y^2=x^2 x^2+4 x^2

Step-by-step solution

aligned & d y d x = x^2+y^2 x y = x y + y x & Let x y =v y= v x & d y d x = v-x ( d v d x ) v^2 & v-x ( d v d x ) v^2 =v+ 1 v 1 v - ( x v^2 ) d v d x =v+ 1 v & d v v^3 =- d x x & -1 2 v^2 =- x-c 1 2 v^2 = x+c & y^2 2 x^2 = x + c y ^2= x ^2 x ^2+2 x ^2 c & We have y (1)=-2 & 4=0+2 c c=2 & y ^2= x ^2 x ^2+4 x ^2 & aligned

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