Sr Examen
Ecuación diferencial y'=y-x/y+x
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Solución
Ha introducido
[src]
d x --(y(x)) = x - ---- + y(x) dx y(x)
$$\frac{d}{d x} y{\left(x \right)} = x - \frac{x}{y{\left(x \right)}} + y{\left(x \right)}$$
y' = x - x/y + y
Respuesta
[src]
/ / 1 \ \
| 6*|1 - --| |
| / 1 \ 3 \ C1/ |
/ / 1 \\ | | 1 + --- / 1 \| 1 + --- - ---------- / 3 \|
| 2*|1 - --|| | | 2 6*|1 - --|| 2 C1 2*|-2 + --||
3 / / 1 \\ 4 | / 1 \ / 1 \ / 1 \ \ C1/| 5 | | 1 2 C1 \ C1/| C1 / 1 \ / 1 \ \ C1/|
2 / 1 \ x *|1 + C1*|1 + ---|| x *|C1*|1 - ---| + |1 + ---|*|1 - --| + ----------| x *|C1*|1 + --- + --- + ------- - ----------| + -------------------- + |1 - --|*|1 - ---| + -----------|
x *|1 + C1 - --| | | 2|| | | 2| | 2| \ C1/ 2 | | | 2 4 2 3 | C1 \ C1/ | 2| 2 |
\ C1/ \ \ C1 // \ \ C1 / \ C1 / C1 / \ \ C1 C1 C1 C1 / \ C1 / C1 / / 6\
y(x) = C1 + C1*x + ---------------- + --------------------- + --------------------------------------------------- + -------------------------------------------------------------------------------------------------------- + O\x /
2 6 24 120
$$y{\left(x \right)} = \frac{x^{2} \left(C_{1} + 1 - \frac{1}{C_{1}}\right)}{2} + \frac{x^{3} \left(C_{1} \left(1 + \frac{1}{C_{1}^{2}}\right) + 1\right)}{6} + \frac{x^{4} \left(C_{1} \left(1 - \frac{1}{C_{1}^{2}}\right) + \left(1 + \frac{1}{C_{1}^{2}}\right) \left(1 - \frac{1}{C_{1}}\right) + \frac{2 \left(1 - \frac{1}{C_{1}}\right)}{C_{1}^{2}}\right)}{24} + \frac{x^{5} \left(C_{1} \left(1 + \frac{1 + \frac{1}{C_{1}^{2}}}{C_{1}^{2}} + \frac{1}{C_{1}^{2}} - \frac{6 \left(1 - \frac{1}{C_{1}}\right)}{C_{1}^{3}} + \frac{2}{C_{1}^{4}}\right) + \left(1 - \frac{1}{C_{1}^{2}}\right) \left(1 - \frac{1}{C_{1}}\right) + \frac{1 - \frac{6 \left(1 - \frac{1}{C_{1}}\right)}{C_{1}} + \frac{3}{C_{1}^{2}}}{C_{1}} + \frac{2 \left(-2 + \frac{3}{C_{1}}\right)}{C_{1}^{2}}\right)}{120} + C_{1} + C_{1} x + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.1722455474165963)
(-5.555555555555555, 1.2761587391414675)
(-3.333333333333333, 1.6374246530130878)
(-1.1111111111111107, 4.72396298078157)
(1.1111111111111107, 41.09087006656395)
(3.333333333333334, 394.1530388760448)
(5.555555555555557, 3670.5589032669377)
(7.777777777777779, 33922.94515463598)
(10.0, 313104.6465164829)
(10.0, 313104.6465164829)