APFIVE Ordering Values of a Particular Solution
The particular solution to the differential equation $$\frac{dy}{dx}=\frac{4x}{y}$$ with the initial condition $$y(0)=5$$ is given by $$y=\sqrt{4x^2+25}$$. Based on the table of values below, which of the following lists the $$x$$-values 0, 1, 2, and 3 in increasing order of their corresponding $$y$$-values?
| $$x$$ | $$y = \sqrt{4x^2+25}$$ |
|---|---|
| 0 | $$\sqrt{25}=5$$ |
| 1 | $$\sqrt{29}$$ |
| 2 | $$\sqrt{41}$$ |
| 3 | $$\sqrt{61}$$ |
A
3,2,1,0
B
1,0,2,3
C
0,1,2,3
D
0,2,1,3
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