Sr Examen
Ecuación diferencial (3x^2-y)dx+(3y^2-x)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d 2 d
-y(x) + 3*x - x*--(y(x)) + 3*y (x)*--(y(x)) = 0
dx dx
$$3 x^{2} - x \frac{d}{d x} y{\left(x \right)} + 3 y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} = 0$$
3*x^2 - x*y' + 3*y^2*y' - y = 0
Respuesta
[src]
3 / 2 \ 4 / 8 \
x *|-2 - ------| x *|8 + ------|
| 3| | 3|
x \ 27*C1 / \ 27*C1 / / 6\
y(x) = C1 + ---- + ---------------- + --------------- + O\x /
3*C1 2 4
6*C1 72*C1
$$y{\left(x \right)} = \frac{x^{4} \left(8 + \frac{8}{27 C_{1}^{3}}\right)}{72 C_{1}^{4}} + \frac{x^{3} \left(-2 - \frac{2}{27 C_{1}^{3}}\right)}{6 C_{1}^{2}} + \frac{x}{3 C_{1}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -7.727638373569286)
(-5.555555555555555, -9.164452811664175)
(-3.333333333333333, -9.735010027006766)
(-1.1111111111111107, -9.931772223677678)
(1.1111111111111107, -10.015236179641624)
(3.333333333333334, -10.206172376895704)
(5.555555555555557, -10.693921847004619)
(7.777777777777779, -11.579533209277983)
(10.0, -12.847432136299549)
(10.0, -12.847432136299549)