Sr Examen
Ecuación diferencial x^3(dy/dx)-xy=2*x^7*y^4
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Solución
Ha introducido
[src]
3 d 7 4 x *--(y(x)) - x*y(x) = 2*x *y (x) dx
$$x^{3} \frac{d}{d x} y{\left(x \right)} - x y{\left(x \right)} = 2 x^{7} y^{4}{\left(x \right)}$$
x^3*y' - x*y = 2*x^7*y^4
Respuesta
[src]
_____________________________________________________________________
3 ____ / -1
y(x) = \/ 20 * / -------------------------------------------------------------------
/ 3 3
/ - / pi*I\ -
/ 2 4 3 5 x |3*e | x
3 / - 27*x - 18*x + 18*x + 24*x + 81*x + C1*e + 243*Ei|-------|*e
\/ \ x /
$$y{\left(x \right)} = \sqrt[3]{20} \sqrt[3]{- \frac{1}{C_{1} e^{\frac{3}{x}} + 24 x^{5} - 18 x^{4} + 18 x^{3} - 27 x^{2} + 81 x + 243 e^{\frac{3}{x}} \operatorname{Ei}{\left(\frac{3 e^{i \pi}}{x} \right)}}}$$
_____________________________________________________________________
3 ____ / -1 / ___\
\/ 20 * / ------------------------------------------------------------------- *\-1 - I*\/ 3 /
/ 3 3
/ - / pi*I\ -
/ 2 4 3 5 x |3*e | x
3 / - 27*x - 18*x + 18*x + 24*x + 81*x + C1*e + 243*Ei|-------|*e
\/ \ x /
y(x) = ---------------------------------------------------------------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{20} \sqrt[3]{- \frac{1}{C_{1} e^{\frac{3}{x}} + 24 x^{5} - 18 x^{4} + 18 x^{3} - 27 x^{2} + 81 x + 243 e^{\frac{3}{x}} \operatorname{Ei}{\left(\frac{3 e^{i \pi}}{x} \right)}}} \left(-1 - \sqrt{3} i\right)}{2}$$
_____________________________________________________________________
3 ____ / -1 / ___\
\/ 20 * / ------------------------------------------------------------------- *\-1 + I*\/ 3 /
/ 3 3
/ - / pi*I\ -
/ 2 4 3 5 x |3*e | x
3 / - 27*x - 18*x + 18*x + 24*x + 81*x + C1*e + 243*Ei|-------|*e
\/ \ x /
y(x) = ---------------------------------------------------------------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{20} \sqrt[3]{- \frac{1}{C_{1} e^{\frac{3}{x}} + 24 x^{5} - 18 x^{4} + 18 x^{3} - 27 x^{2} + 81 x + 243 e^{\frac{3}{x}} \operatorname{Ei}{\left(\frac{3 e^{i \pi}}{x} \right)}}} \left(-1 + \sqrt{3} i\right)}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
Bernoulli
lie group
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1565.1132752912144)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 2.653805977506925e-32)
(7.777777777777779, 8.3882435673367e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)