Sr Examen
Ecuación diferencial xdy=x^(4)dx+2x^(6)dx/3y+2ydx
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
6 d 4 2*x *y(x) x*--(y(x)) = x + 2*y(x) + --------- dx 3
$$x \frac{d}{d x} y{\left(x \right)} = \frac{2 x^{6} y{\left(x \right)}}{3} + x^{4} + 2 y{\left(x \right)}$$
x*y' = 2*x^6*y/3 + x^4 + 2*y
Respuesta
[src]
/ 6\
2/3 3 ___ | x |
C1 + 27*2 *\/ 3 *Gamma(1/3)*Gamma(5/6)*lowergamma|1/3, --|
\ 9 /
y(x) = --------------------------------------------------------------------------------
/ / pi*I 6\ / 6\\
____ | |e x | | x ||
12*\/ pi *|Gamma(-1/3)*lowergamma|-----, --| - 9*Gamma(2/3)*lowergamma|2/3, --||
\ \ 3 9 / \ 9 //
$$y{\left(x \right)} = \frac{C_{1} + 27 \cdot 2^{\frac{2}{3}} \sqrt[3]{3} \Gamma\left(\frac{1}{3}\right) \Gamma\left(\frac{5}{6}\right) \gamma\left(\frac{1}{3}, \frac{x^{6}}{9}\right)}{12 \sqrt{\pi} \left(- 9 \Gamma\left(\frac{2}{3}\right) \gamma\left(\frac{2}{3}, \frac{x^{6}}{9}\right) + \Gamma\left(- \frac{1}{3}\right) \gamma\left(\frac{e^{i \pi}}{3}, \frac{x^{6}}{9}\right)\right)}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st linear
Bernoulli
almost linear
lie group
1st exact Integral
1st linear Integral
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -0.024795248291199057)
(-5.555555555555555, -0.04859008665453305)
(-3.333333333333333, -0.13441586427204852)
(-1.1111111111111107, -0.5202220003852714)
(1.1111111111111107, -0.5201533203374495)
(3.333333333333334, 1.5449469787101562e+27)
(5.555555555555557, 3.854045095460155e-57)
(7.777777777777779, 8.388243571811068e+296)
(10.0, 1.0759798446059127e-282)
(10.0, 1.0759798446059127e-282)