Sr Examen
Ecuación diferencial xy'-3y+(x^4)(y^4)=0
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Solución
Ha introducido
[src]
d 4 4
-3*y(x) + x*--(y(x)) + x *y (x) = 0
dx
$$x^{4} y^{4}{\left(x \right)} + x \frac{d}{d x} y{\left(x \right)} - 3 y{\left(x \right)} = 0$$
x^4*y^4 + x*y' - 3*y = 0
Respuesta
[src]
_______________
/ 9
3 ____ / C1*x
y(x) = \/ 13 * / -------------
3 / 13
\/ -1 + 3*C1*x
$$y{\left(x \right)} = \sqrt[3]{13} \sqrt[3]{\frac{C_{1} x^{9}}{3 C_{1} x^{13} - 1}}$$
_______________
/ 9
3 ____ / C1*x / ___\
\/ 13 * / ------------- *\-1 + I*\/ 3 /
3 / 13
\/ -1 + 3*C1*x
y(x) = -------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{13} \sqrt[3]{\frac{C_{1} x^{9}}{3 C_{1} x^{13} - 1}} \left(-1 + \sqrt{3} i\right)}{2}$$
_______________
/ 9
3 ____ / C1*x / ___\
\/ 13 * / ------------- *\-1 - I*\/ 3 /
3 / 13
\/ -1 + 3*C1*x
y(x) = -------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{13} \sqrt[3]{\frac{C_{1} x^{9}}{3 C_{1} x^{13} - 1}} \left(-1 - \sqrt{3} i\right)}{2}$$
Gráfico para el problema de Cauchy
Clasificación
separable reduced
lie group
separable reduced Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1565.011919143093)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 4.3149409499051355e-61)
(7.777777777777779, 8.388243567736643e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)