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AP EAMCET202119 Aug 2021Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation d 2 y d x 2 + y = 0 is

Options

  1. Ay = 3 sin ⁡ x + 4 cos ⁡ x
  2. By = x 2
  3. Cy = x + 2
  4. Dy = log ⁡ x

Correct answer

A. y = 3 sin ⁡ x + 4 cos ⁡ x

Step-by-step solution

Given, d 2 y d x 2 + y = 0 We will check if y = 3 sin x + 4 cos x is solution of the differential equation. Differentiating this w.r.t x d y d x = 3 cos x - 4 sin x Again differentiating w.r.t. x d 2 y d x 2 = - 3 sin x - 4 cos x ⇒ d 2 y d x 2 = - 3 sin x + 4 cos x = - y ⇒ d 2 y d x 2 + y = 0 Hence, y = 3 sin x + 4 cos x is solution of the differential equation d 2 y d x 2 + y = 0 . Alternative Method: Given is a second-order linear ordinary differential equation. Its general solution is of the form y =

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