Sr Examen
Ecuación diferencial ydx+(-(y^2)/3-2*x)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d
y (x)*--(y(x))
d dx
- 2*x*--(y(x)) - -------------- + y(x) = 0
dx 3
$$- 2 x \frac{d}{d x} y{\left(x \right)} - \frac{y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{3} + y{\left(x \right)} = 0$$
-2*x*y' - y^2*y'/3 + y = 0
Respuesta
[src]
4 2 3 5
3*x 9261*x 27*x 225*x 531441*x / 6\
y(x) = C1 + --- - ------- - ----- + ------ + --------- + O\x /
C1 7 3 5 9
8*C1 2*C1 2*C1 40*C1
$$y{\left(x \right)} = \frac{531441 x^{5}}{40 C_{1}^{9}} - \frac{9261 x^{4}}{8 C_{1}^{7}} + \frac{225 x^{3}}{2 C_{1}^{5}} - \frac{27 x^{2}}{2 C_{1}^{3}} + \frac{3 x}{C_{1}} + C_{1} + O\left(x^{6}\right)$$
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, 0.6606526395299006)
(-5.555555555555555, 0.5574686203074958)
(-3.333333333333333, 0.4307790624106404)
(-1.1111111111111107, 0.24744061481279114)
(1.1111111111111107, -0.01595021586386266)
(3.333333333333334, -0.02762598213656725)
(5.555555555555557, -0.03566463082598074)
(7.777777777777779, -0.04219868041360821)
(10.0, -0.04784856959987113)
(10.0, -0.04784856959987113)