Sr Examen
Ecuación diferencial ((2y-cos(2x))dy/dx)+2x+2ysin(2x)=0
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Solución
Ha introducido
[src]
d
2*x + (-cos(2*x) + 2*y(x))*--(y(x)) + 2*sin(2*x)*y(x) = 0
dx
$$2 x + \left(2 y{\left(x \right)} - \cos{\left(2 x \right)}\right) \frac{d}{d x} y{\left(x \right)} + 2 y{\left(x \right)} \sin{\left(2 x \right)} = 0$$
2*x + (2*y - cos(2*x))*y' + 2*y*sin(2*x) = 0
Respuesta
[src]
/ / 1 2*C1 \\
| 3*(-1 - 2*C1)*|-1 + --------- + ---------||
4 | 3 6*C1 \ -1 + 2*C1 -1 + 2*C1/|
2 x *|2*C1 + --------- + --------- + ------------------------------------------|
x *(-1 - 2*C1) \ -1 + 2*C1 -1 + 2*C1 -1 + 2*C1 / / 6\
y(x) = C1 + -------------- + ------------------------------------------------------------------------------ + O\x /
-1 + 2*C1 3*(-1 + 2*C1)
$$y{\left(x \right)} = \frac{x^{2} \left(- 2 C_{1} - 1\right)}{2 C_{1} - 1} + \frac{x^{4} \left(2 C_{1} + \frac{6 C_{1}}{2 C_{1} - 1} + \frac{3 \left(- 2 C_{1} - 1\right) \left(\frac{2 C_{1}}{2 C_{1} - 1} - 1 + \frac{1}{2 C_{1} - 1}\right)}{2 C_{1} - 1} + \frac{3}{2 C_{1} - 1}\right)}{3 \left(2 C_{1} - 1\right)} + C_{1} + O\left(x^{6}\right)$$
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, 5.8308927212853785)
(-5.555555555555555, 8.388039952157705)
(-3.333333333333333, 9.916743321220666)
(-1.1111111111111107, 9.652429815397864)
(1.1111111111111107, 9.652429920211567)
(3.333333333333334, 9.916742993600838)
(5.555555555555557, 8.388039961059079)
(7.777777777777779, 5.830892508618567)
(10.0, 0.7499933280569419)
(10.0, 0.7499933280569419)