Sr Examen
Ecuación diferencial dx*(3*x^2*y-y)+dy*(x^3-x+2*y)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
3 d d d 2
-y(x) + x *--(y(x)) - x*--(y(x)) + 2*--(y(x))*y(x) + 3*x *y(x) = 0
dx dx dx
$$x^{3} \frac{d}{d x} y{\left(x \right)} + 3 x^{2} y{\left(x \right)} - x \frac{d}{d x} y{\left(x \right)} + 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} = 0$$
x^3*y' + 3*x^2*y - x*y' + 2*y*y' - y = 0
Respuesta
[src]
_____________________
3 / 2 6 4
x x \/ C1 + x + x - 2*x
y(x) = - - -- - ------------------------
2 2 2
$$y{\left(x \right)} = - \frac{x^{3}}{2} + \frac{x}{2} - \frac{\sqrt{C_{1} + x^{6} - 2 x^{4} + x^{2}}}{2}$$
_____________________
/ 2 6 4 3
x \/ C1 + x + x - 2*x x
y(x) = - + ------------------------ - --
2 2 2
$$y{\left(x \right)} = - \frac{x^{3}}{2} + \frac{x}{2} + \frac{\sqrt{C_{1} + x^{6} - 2 x^{4} + x^{2}}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.6089875399776372)
(-5.555555555555555, 4.599371961889952)
(-3.333333333333333, 27.238540378154102)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 9.144805860439919e-71)
(7.777777777777779, 8.388243567717373e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)