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MHT CET202415 May 2024Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation d y d x = 3 e^ 2 x +3 e^ 4 x . e^x+e^ -x is

Options

  1. Ay= e ^ -3 x + c , where c is a constant of integration.
  2. By= e ^x+ c , where c is a constant of integration.
  3. Cy= e ^ 3 x + c , where c is a constant of integration.
  4. Dy= e ^ -x + c , where c is a constant of integration.

Correct answer

C. y= e ^ 3 x + c , where c is a constant of integration.

Step-by-step solution

aligned & d y ~d x = 3 e ^ 2 x +3 e ^ 4 x e ^x+ e ^ -x & ~d y ~d x = 3 e ^ 2 x (1+ e ^ 2 x ) ( e ^ 2 x +1 e ^x ) & d y ~d x =3 e ^ 2 x e ^x & ~d y=3 e ^ 3 x ~d x aligned Integrating on both sides, we get y= e ^ 3 x + c

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