Sr Examen
Ecuación diferencial (x^3)+(ysin(x))+(cos(x)+2y)dy/dx=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
3 d
x + (2*y(x) + cos(x))*--(y(x)) + sin(x)*y(x) = 0
dx
$$x^{3} + \left(2 y{\left(x \right)} + \cos{\left(x \right)}\right) \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \sin{\left(x \right)} = 0$$
x^3 + (2*y + cos(x))*y' + y*sin(x) = 0
Respuesta
[src]
/ / 2*C1 \\
| 3*C1*|-1 + --------||
4 | 3*C1 \ 1 + 2*C1/|
2 x *|-6 + C1 - -------- - --------------------|
C1*x \ 1 + 2*C1 1 + 2*C1 / / 6\
y(x) = C1 - ------------ + ---------------------------------------------- + O\x /
2*(1 + 2*C1) 24*(1 + 2*C1)
$$y{\left(x \right)} = \frac{x^{4} \left(C_{1} - \frac{3 C_{1} \left(\frac{2 C_{1}}{2 C_{1} + 1} - 1\right)}{2 C_{1} + 1} - \frac{3 C_{1}}{2 C_{1} + 1} - 6\right)}{24 \left(2 C_{1} + 1\right)} + C_{1} - \frac{C_{1} x^{2}}{2 \left(2 C_{1} + 1\right)} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 40.67998807295914)
(-5.555555555555555, 48.52210625454924)
(-3.333333333333333, 49.762699517979115)
(-1.1111111111111107, 50.78454208946364)
(1.1111111111111107, 50.78454200066329)
(3.333333333333334, 49.762695744063016)
(5.555555555555557, 48.52210364029873)
(7.777777777777779, 40.679982929218916)
(10.0, 0.7490474513390548)
(10.0, 0.7490474513390548)