Which of the following is a solution to the second order differential equation LaTeX: y''=-4y y ″ = - 4 y? To answer this question, attempt to verify each of the following proposed solutions. a. LaTeX: y=/sin2t y = sin ⁡ 2 t b. LaTeX: y=-/frac{2}{3}t^3 y = - 2 3 t 3 c. LaTeX: y=/cos2t y = cos ⁡ 2 t d. LaTeX: y=e^{2t} y = e 2 t e. LaTeX: y=/frac{y''}{-4}

Question

Jamie Odonnell

Mathematics

25 May, 17:29

Which of the following is a solution to the second order differential equation LaTeX: y''=-4y y ″ = - 4 y? To answer this question, attempt to verify each of the following proposed solutions. a. LaTeX: y=/sin2t y = sin ⁡ 2 t b. LaTeX: y=-/frac{2}{3}t^3 y = - 2 3 t 3 c. LaTeX: y=/cos2t y = cos ⁡ 2 t d. LaTeX: y=e^{2t} y = e 2 t e. LaTeX: y=/frac{y''}{-4}

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Answers (1)

Know the Answer?

Selena Green · Answer 1

y = sin (2t) y = cos (2t)

Step-by-step explanation:

In the case of each of the answers listed above, the second derivative is equal to - 4 times the function, as required by the differential equation.

For y = 2/3t^3, the second derivative is 4t, not - 4y.

For y = e^ (2t), the second derivative is 4y, not - 4y.

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The graph shows the sum of the second derivative and 4y is zero for the answers indicated above, and not zero for the other two proposed answers.