Sr Examen
Ecuación diferencial dx+(9*x^2+5*e^6*y-3)^1/2*dy=0
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Solución
Ha introducido
[src]
_______________________
/ 2 6 d
1 + \/ -3 + 9*x + 5*e *y(x) *--(y(x)) = 0
dx
$$\sqrt{9 x^{2} + 5 y{\left(x \right)} e^{6} - 3} \frac{d}{d x} y{\left(x \right)} + 1 = 0$$
sqrt(9*x^2 + 5*y*exp(6) - 3)*y' + 1 = 0
Respuesta
[src]
/ / 12 \ \
| | 21875*e | 12|
| |-3375 + -----------------|*e |
| | 2| |
/ 12 \ | 12 | / 6\ | | / 12 \
3 | 25*e | 5 | 7875*e \ 2*\-3 + 5*C1*e / / | 4 | 875*e | 6
x *|9 - ---------------| x *|-729 + ----------------- - -------------------------------| x *|225 - -----------------|*e
| 2| | 2 2 | | 2|
2 6 | / 6\ | | / 6\ / 6\ | | / 6\ |
x 5*x *e \ \-3 + 5*C1*e / / \ 2*\-3 + 5*C1*e / \-3 + 5*C1*e / / \ 2*\-3 + 5*C1*e / / / 6\
y(x) = C1 - ----------------- - ----------------- + ------------------------ + --------------------------------------------------------------- + ------------------------------- + O\x /
______________ 2 3/2 5/2 3
/ 6 / 6\ / 6\ / 6\ / 6\
\/ -3 + 5*C1*e 4*\-3 + 5*C1*e / 6*\-3 + 5*C1*e / 120*\-3 + 5*C1*e / 24*\-3 + 5*C1*e /
$$y{\left(x \right)} = - \frac{x}{\sqrt{5 C_{1} e^{6} - 3}} - \frac{5 x^{2} e^{6}}{4 \left(5 C_{1} e^{6} - 3\right)^{2}} + \frac{x^{3} \left(9 - \frac{25 e^{12}}{\left(5 C_{1} e^{6} - 3\right)^{2}}\right)}{6 \left(5 C_{1} e^{6} - 3\right)^{\frac{3}{2}}} + \frac{x^{4} \left(225 - \frac{875 e^{12}}{2 \left(5 C_{1} e^{6} - 3\right)^{2}}\right) e^{6}}{24 \left(5 C_{1} e^{6} - 3\right)^{3}} + \frac{x^{5} \left(- \frac{\left(-3375 + \frac{21875 e^{12}}{2 \left(5 C_{1} e^{6} - 3\right)^{2}}\right) e^{12}}{\left(5 C_{1} e^{6} - 3\right)^{2}} - 729 + \frac{7875 e^{12}}{2 \left(5 C_{1} e^{6} - 3\right)^{2}}\right)}{120 \left(5 C_{1} e^{6} - 3\right)^{\frac{5}{2}}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7023127494963944)
(-5.555555555555555, 0.6493419088245976)
(-3.333333333333333, 0.5904973399910064)
(-1.1111111111111107, 0.5255068865055195)
(1.1111111111111107, 0.45484537166892614)
(3.333333333333334, 0.38025420896968354)
(5.555555555555557, 0.3048812260906001)
(7.777777777777779, 0.23243439273888922)
(10.0, 0.1657203013976447)
(10.0, 0.1657203013976447)