Sr Examen
Ecuación diferencial sqrt(y'+1)(yy''-(y')^2)=yy'sqrt(yy')
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Solución
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______________ / 2 2 \ _______________
/ d | /d \ d | / d d
/ 1 + --(y(x)) *|- |--(y(x))| + ---(y(x))*y(x)| = / --(y(x))*y(x) *--(y(x))*y(x)
\/ dx | \dx / 2 | \/ dx dx
\ dx /
$$\left(y{\left(x \right)} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - \left(\frac{d}{d x} y{\left(x \right)}\right)^{2}\right) \sqrt{\frac{d}{d x} y{\left(x \right)} + 1} = \sqrt{y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
(y*y'' - y'^2)*sqrt(y' + 1) = sqrt(y*y')*y*y'