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MHT CET202314 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If the slope of the tangent of the curve at any point is equal to -y+ e ^ -x , then the equation of the curve passing through origin is

Options

  1. Ay+x e ^x=0
  2. By e ^x+x=0
  3. Cy e ^x-x=0
  4. Dy-x e ^x=0

Correct answer

C. y e ^x-x=0

Step-by-step solution

aligned & d y ~d x =-y+ e ^ -x & d y ~d x +y= e ^ -x & I.F. = e ^ dx = e ^x aligned Solution of the given equation is gathered y e ^x= e ^x e ^ -x ~d x+ c y e ^x= d x c y e ^x=x+ c gathered Since the curve passes through (0,0) . array ll & 0=0+ c & c =0 & y e ^x=x & y e ^x-x^2=0 array

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