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Solve the equation $ y' = x \sqrt {x^2 + 1/(ye^y)} $ and graph several members of the family of solution (if your CAS does implicit plots). How does the solution curve change as the constant $ C $ varies?

$e^{y}(y-1)=\frac{1}{3}\left(x^{2}+1\right)^{3 / 2}+C$

Differential Equations

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Missouri State University

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