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Solve a first-order nonlinear ordinary differential equation with W|A?

Posted 1 month ago
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https://www.wolframalpha.com/input/?i=(dy%2Fdx)%5E2)%2B1%3Dy%5E2

says (dy/dx)^2)+1=y^2 => y=cosh(x+c), y=cosh(x-c)

while it should be y=┬▒cosh(x+c), y=┬▒1

The two answers provided are same, and some results don't show

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