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}

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.

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d