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# Show that$y = \sin \left( \tan ^ { - 1 } x + C \right)$is the general solution of$y ^ { \prime } = \sqrt { 1 - y ^ { 2 } } / \left( 1 + x ^ { 2 } \right).$Then use the addition formula for the sine function to show that the general solution may be written$y = \frac { ( \cos C ) x + \sin C } { \sqrt { 1 + x ^ { 2 } } }$

Solution

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Step 1
1 of 4

We are given the equation:

$y'=\dfrac{\sqrt{1-y^2}}{1+x^2}$

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