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MHT CET20243 May 2024Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation x y ~d y= (x e ^x x+ e ^x ) d x is given by

Options

  1. Ay= e ^x+ cog x , where c is a constant of integration.
  2. By= e ^x x+ c , where c is a constant of integration.
  3. Ce ^x y= x+ c , where c is a constant of integration,
  4. Dy= ce ^x+ x , where c is a constant of integration.

Correct answer

B. y= e ^x x+ c , where c is a constant of integration.

Step-by-step solution

aligned & x y ~d y= (x e ^x x+ e ^x ) d x & y ~d y= e ^x ( x+ 1 x ) d x aligned Integrating on both sides, we get y= e ^x x+ c

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