Sr Examen
Ecuación diferencial x''=(siny*x'^3+2*x*x'^2+siny*x'+2x)/(x^2+cosy+2)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
3 2
/d \ d /d \
2 2*x(y) + |--(x(y))| *sin(y) + --(x(y))*sin(y) + 2*|--(x(y))| *x(y)
d \dy / dy \dy /
---(x(y)) = ------------------------------------------------------------------
2 2
dy 2 + x (y) + cos(y)
$$\frac{d^{2}}{d y^{2}} x{\left(y \right)} = \frac{2 x{\left(y \right)} \left(\frac{d}{d y} x{\left(y \right)}\right)^{2} + 2 x{\left(y \right)} + \sin{\left(y \right)} \left(\frac{d}{d y} x{\left(y \right)}\right)^{3} + \sin{\left(y \right)} \frac{d}{d y} x{\left(y \right)}}{x^{2}{\left(y \right)} + \cos{\left(y \right)} + 2}$$
x'' = (2*x*x'^2 + 2*x + sin(y)*x'^3 + sin(y)*x')/(x^2 + cos(y) + 2)
Clasificación
factorable