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AP EAMCET202423 May 2024Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation e^x y d x+e^x d y+x d x=0 is

Options

  1. Ae^x+y x^2=c
  2. B2 y e^x+x^2=c
  3. Cy e^x+x^2 e^y=c
  4. De^x+x e^y=c

Correct answer

B. 2 y e^x+x^2=c

Step-by-step solution

e^x y d x+e^x d y+x d x=0 (e^x y+x ) d x+e^x d y=0 d y d x +y=-x e^ -x I.F. =e^ d x =e^x Solution : aligned & y e^x= -x d x+C₁ y e^x= -x^2 2 +C₁ & 2 y e^x+x^2=C aligned

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