Sr Examen
Ecuación diferencial ydx+xdy=-(1/1+1xy)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d d d x*--(y(x)) + y(x) = - --(y(x)) - x*--(y(x))*y(x) dx dx dx
$$x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = - x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - \frac{d}{d x} y{\left(x \right)}$$
x*y' + y = -x*y*y' - y'
Respuesta
[src]
2 3 / 2\ 4 / 3 2 \ 5 / 4 2 3 / 2 \ 2 2 2 2 2 / 2 \ \
C1*x *(2 + C1) C1*x *\-4 - 5*C1 - 2*(-1 - C1) / C1*x *\3 - 3*(-1 - C1) + 3*(-1 - C1) + 8*C1 - (1 + C1)*(-1 - C1) - (1 + 2*C1)*(-1 - C1) - (1 + 3*C1)*(-1 - C1) - 4*C1*(-1 - C1)/ C1*x *\-4 - 12*(-1 - C1) - 11*C1 - 9*(-1 - C1) + 12*(-1 - C1) - (-1 - C1)*\-2 - (-1 - C1) - 5*C1 + 2*C1*(-1 - C1)/ - 27*C1*(-1 - C1) - 3*C1*(1 + 2*C1) - 3*(-1 - C1) *(1 + 2*C1) - 3*(-1 - C1) *(1 + 3*C1) - 3*(-1 - C1) *(1 + 4*C1) - 2*C1*(1 + C1) - 2*(-1 - C1) *(1 + C1) - 2*(-1 - C1)*\-1 - (-1 - C1) - 3*C1 + 2*C1*(-1 - C1)/ + 2*C1*(-7 - 6*C1) + 2*(1 + C1)*(-1 - C1) + 3*C1*(-3 - 2*C1) + 3*(1 + 2*C1)*(-1 - C1) + 6*C1*(-2 - 3*C1) + 26*C1*(-1 - C1)/ / 6\
y(x) = C1 - C1*x + -------------- + -------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x /
2 6 12 60
$$y{\left(x \right)} = C_{1} - C_{1} x + \frac{C_{1} x^{2} \left(C_{1} + 2\right)}{2} + \frac{C_{1} x^{3} \left(- 5 C_{1} - 2 \left(- C_{1} - 1\right)^{2} - 4\right)}{6} + \frac{C_{1} x^{4} \left(- 4 C_{1} \left(- C_{1} - 1\right) + 8 C_{1} - 3 \left(- C_{1} - 1\right)^{3} + 3 \left(- C_{1} - 1\right)^{2} - \left(- C_{1} - 1\right) \left(C_{1} + 1\right) - \left(- C_{1} - 1\right) \left(2 C_{1} + 1\right) - \left(- C_{1} - 1\right) \left(3 C_{1} + 1\right) + 3\right)}{12} + \frac{C_{1} x^{5} \left(2 C_{1} \left(- 6 C_{1} - 7\right) + 6 C_{1} \left(- 3 C_{1} - 2\right) + 3 C_{1} \left(- 2 C_{1} - 3\right) - 27 C_{1} \left(- C_{1} - 1\right)^{2} + 26 C_{1} \left(- C_{1} - 1\right) - 2 C_{1} \left(C_{1} + 1\right) - 3 C_{1} \left(2 C_{1} + 1\right) - 11 C_{1} - 12 \left(- C_{1} - 1\right)^{4} + 12 \left(- C_{1} - 1\right)^{3} - 2 \left(- C_{1} - 1\right)^{2} \left(C_{1} + 1\right) - 3 \left(- C_{1} - 1\right)^{2} \left(2 C_{1} + 1\right) - 3 \left(- C_{1} - 1\right)^{2} \left(3 C_{1} + 1\right) - 3 \left(- C_{1} - 1\right)^{2} \left(4 C_{1} + 1\right) - 9 \left(- C_{1} - 1\right)^{2} + 2 \left(- C_{1} - 1\right) \left(C_{1} + 1\right) + 3 \left(- C_{1} - 1\right) \left(2 C_{1} + 1\right) - \left(- C_{1} - 1\right) \left(2 C_{1} \left(- C_{1} - 1\right) - 5 C_{1} - \left(- C_{1} - 1\right)^{2} - 2\right) - 2 \left(- C_{1} - 1\right) \left(2 C_{1} \left(- C_{1} - 1\right) - 3 C_{1} - \left(- C_{1} - 1\right)^{2} - 1\right) - 4\right)}{60} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8698757121154025)
(-5.555555555555555, 1.0482637832725263)
(-3.333333333333333, 1.3597742628424976)
(-1.1111111111111107, 2.2307220067204505)
(1.1111111111111107, 248.74549721769986)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 5.107659831618641e-38)
(7.777777777777779, 8.388243566958191e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)