Find the Solution to the Differential Equation $x y ^ { \prime } = \sqrt { 1 - y ^ { 2 } } , x > 0$

question 149

Essay

Find the solution to the differential equation $x y ^ { \prime } = \sqrt { 1 - y ^ { 2 } } , x > 0$ that satisfies the initial condition $y ( 1 ) = 1$ .

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Definitions:

Pearson Correlation

A measure of the linear correlation between two variables, quantifying the degree to which their movements are associated.

Approximate Normal

Describes a distribution that is close to, but not exactly, a normal distribution.

Sample Size

Refers to the number of observations or elements chosen from a population for the purpose of statistical analysis.

Approximate Normal

Describes data or distributions that are nearly, but not perfectly, normally distributed, exhibiting characteristics close to that of a bell-shaped curve.