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BITSAT2018MathematicsDifferential EquationsActual

The solution of the differential equation d 2 y d x 2 = sin 3 x + e x + x 2 when y 1 0 = 1 and y 0 = 0 , is

Options

  1. A- sin 3 x 9 + e x + x 4 12 + 1 3 x - 1
  2. B- sin 3 x 9 + e x + x 4 12 + 1 3 x
  3. C- cos 3 x 9 + e x + x 4 12 + 1 3 x + 1
  4. DNone of the above

Correct answer

A. - sin 3 x 9 + e x + x 4 12 + 1 3 x - 1

Step-by-step solution

Integrating the given differential equation, we have d y d x = - cos 3 x 3 + e x + x 3 3 + C 1 But y 1 0 = 1 So, 1 = - 1 3 + 1 + C 1 ⇒ C 1 = 1 3 ∴   d y d x = - cos 3 x 3 + e x + x 3 3 + 1 3 Again integrating, we get y = - sin 3 x 9 + e x + x 4 12 + 1 3 x + C 2 But y 0 = 0 , so 0 = 0 + 1 + C 2 ⇒ C 2 = - 1 Thus, y = - sin 3 x 9 + e x + x 4 12 + 1 3 x - 1 Hence, option (a) correct.

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