Question

f"'+ff"-f'^2=0 f(0)=0, f'(0)=1, f(inf)=0
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Answer 1

x2 − 2x = −1 =⇒ (x − 1)(x − 1)=0=⇒ x = 1. Plugging into the equation for the curve we see that y = 1/3 at this point.