Sr Examen
Ecuación diferencial ysin(2x)dx-(1+y^2+cos^2(x))dy=0
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Solución
Ha introducido
[src]
d 2 d 2 d - --(y(x)) + sin(2*x)*y(x) - cos (x)*--(y(x)) - y (x)*--(y(x)) = 0 dx dx dx
$$- y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \sin{\left(2 x \right)} - \cos^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - \frac{d}{d x} y{\left(x \right)} = 0$$
-y^2*y' + y*sin(2*x) - cos(x)^2*y' - y' = 0
Respuesta
[src]
/ / 2 \\
| | 2*C1 ||
| 3*|1 - -------||
| | 2||
4 | 3 \ 2 + C1 /|
C1*x *|-2 + ------- + ---------------|
2 | 2 2 |
C1*x \ 2 + C1 2 + C1 / / 6\
y(x) = C1 + ------- + -------------------------------------- + O\x /
2 / 2\
2 + C1 6*\2 + C1 /
$$y{\left(x \right)} = C_{1} + \frac{C_{1} x^{2}}{C_{1}^{2} + 2} + \frac{C_{1} x^{4} \left(-2 + \frac{3 \left(- \frac{2 C_{1}^{2}}{C_{1}^{2} + 2} + 1\right)}{C_{1}^{2} + 2} + \frac{3}{C_{1}^{2} + 2}\right)}{6 \left(C_{1}^{2} + 2\right)} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.0388848965521542)
(-5.555555555555555, 0.8008539541717503)
(-3.333333333333333, 0.6711325730057007)
(-1.1111111111111107, 0.948029339601166)
(1.1111111111111107, 0.9480294320026148)
(3.333333333333334, 0.6711325572839829)
(5.555555555555557, 0.8008539612972184)
(7.777777777777779, 1.0388848512015278)
(10.0, 0.7500000396226204)
(10.0, 0.7500000396226204)