Sr Examen
Ecuación diferencial tgyy''=(y')^2
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Solución
Ha introducido
[src]
2 2 2 2
/d \ / 2/ 2 \\ / 2/ 2 \\ d /d \ 2 / 2/ 2 \\ / 2 \ /d \
|--(y(x))| *\2 + 2*tan \y (x)// + \2 + 2*tan \y (x)//*---(y(x))*y(x) + 8*|--(y(x))| *y (x)*\1 + tan \y (x)//*tan\y (x)/ = |--(y(x))|
\dx / 2 \dx / \dx /
dx
$$8 \left(\tan^{2}{\left(y^{2}{\left(x \right)} \right)} + 1\right) y^{2}{\left(x \right)} \tan{\left(y^{2}{\left(x \right)} \right)} \left(\frac{d}{d x} y{\left(x \right)}\right)^{2} + \left(2 \tan^{2}{\left(y^{2}{\left(x \right)} \right)} + 2\right) y{\left(x \right)} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \left(2 \tan^{2}{\left(y^{2}{\left(x \right)} \right)} + 2\right) \left(\frac{d}{d x} y{\left(x \right)}\right)^{2} = \left(\frac{d}{d x} y{\left(x \right)}\right)^{2}$$
8*(tan(y^2)^2 + 1)*y^2*tan(y^2)*y'^2 + (2*tan(y^2)^2 + 2)*y*y'' + (2*tan(y^2)^2 + 2)*y'^2 = y'^2
Clasificación
factorable