Sr Examen
Ecuación diferencial 2cosydx-(xseny-x^3)dy=0
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Solución
Ha introducido
[src]
3 d d
2*cos(y(x)) + x *--(y(x)) - x*--(y(x))*sin(y(x)) = 0
dx dx
$$x^{3} \frac{d}{d x} y{\left(x \right)} - x \sin{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + 2 \cos{\left(y{\left(x \right)} \right)} = 0$$
x^3*y' - x*sin(y)*y' + 2*cos(y) = 0
Respuesta
[src]
/ ____________________\
| 2 / 4 2 4 |
|x - \/ -1 + x + 4*C1 *x |
y(x) = 2*atan|----------------------------|
| 2 |
\ 1 + 2*C1*x /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(\frac{x^{2} - \sqrt{4 C_{1}^{2} x^{4} + x^{4} - 1}}{2 C_{1} x^{2} + 1} \right)}$$
/ ____________________\
| 2 / 4 2 4 |
|x + \/ -1 + x + 4*C1 *x |
y(x) = 2*atan|----------------------------|
| 2 |
\ 1 + 2*C1*x /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(\frac{x^{2} + \sqrt{4 C_{1}^{2} x^{4} + x^{4} - 1}}{2 C_{1} x^{2} + 1} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7548113363541452)
(-5.555555555555555, 0.7665042972175284)
(-3.333333333333333, 0.8089843779661362)
(-1.1111111111111107, 1.3820403874615919)
(1.1111111111111107, 2.3134191915419935)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 2.6183805095781304e+180)
(7.777777777777779, 8.388243566974611e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)