Question

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}

Answer 1

• y = sin(2t)
• y = cos(2t)

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.