Sr Examen
Ecuación diferencial dx*sqrt(y^3+3)-dy*y=dy*x^3*y
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Solución
Ha introducido
[src]
___________
/ 3 d 3 d
\/ 3 + y (x) - --(y(x))*y(x) = x *--(y(x))*y(x)
dx dx
$$\sqrt{y^{3}{\left(x \right)} + 3} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{3} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
sqrt(y^3 + 3) - y*y' = x^3*y*y'
Respuesta
[src]
_ / | 3 pi*I\ / ___ \
___ 2 |_ |1/2, 2/3 | y (x)*e | ___ |\/ 3 *(-1 + 2*x)|
\/ 3 *y (x)*Gamma(2/3)* | | | -----------| / 2 \ \/ 3 *atan|----------------|
2 1 \ 5/3 | 3 / log\1 + x - x/ log(1 + x) \ 3 /
---------------------------------------------------- = C1 - --------------- + ---------- + ----------------------------
9*Gamma(5/3) 6 3 3
$$\frac{\sqrt{3} y^{2}{\left(x \right)} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{e^{i \pi} y^{3}{\left(x \right)}}{3}} \right)}}{9 \Gamma\left(\frac{5}{3}\right)} = C_{1} + \frac{\log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{3}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st power series
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7418980579892263)
(-5.555555555555555, 0.7218523900736092)
(-3.333333333333333, 0.6437791660688071)
(-1.1111111111111107, -2.115245293614708e-09)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 4.958783545387881e-62)
(7.777777777777779, 8.388243566957436e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)