The explicit solution to the differential equation is y = tan x
<h3>Differential equation</h3>
Given the differential function:

Using the variable separable method;

Integrate both sides of the equation


Using the initial condition y(0) = 0
If x = 0
0 = tan(0 + C)
0 = tanC
C = arctan 0
C = 0
Recall that y = tan (x+C)
y = tan(x+0)
y = tan x
Hence the explicit solution to the differential equation is y = tan x
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Complete question;
<em>The distribution of lengths of salmon from a certain river is approximately normal with a standard deviation of 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution? 26 inches A 28 inches B 30 inches C 33 inches D 34 inches</em>
Option B is correct. The value that is closest to the mean of the distribution is 30inches.
The formula for calculating the z-score is expressed as:

Given the following parameters

If 10 percent of salmon are longer than 30 inches, then:
Using the z table to get the value corresponding to the mean area 0.1.
- The required z-score will be -1.285
Substitute the resulting parameters into the formula to get the mean of the distribution.

Hence the value that is closest to the mean of the distribution is 30inches.
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