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MHT CET20226 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation (1+e^ -x ) (1+y^2 ) d y d x =y^2 which passes through the point (0,1) is

Options

  1. Ay^2+1=y ( ( 1+e^x 2 )+2 )
  2. By^2+1=y ( ( ( 1+e^ -x 2 )+2 ) )
  3. Cy^2=1+y ( 1+e^ -x 2 )
  4. Dy^2=1+y ( 1+e^x 2 )

Correct answer

D. y^2=1+y ( 1+e^x 2 )

Step-by-step solution

aligned & (1+e^ -x ) (1+y^2 ) d y d x =y^2 & 1+y^2 y^2 d y= e^x 1+e^x d x & - 1 y +y= (1+e^x )+ C & -1+y^2=y c (1+e^x ) aligned Putting x=0 and y=1 we get c= 1 2 aligned & -1+y^2=y ( 1+e^x 2 ) & y^2=1+y ( 1+e^x 2 ) aligned

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