Sr Examen
Ecuación diferencial (x+y)sin(y)dx+(xsiny+cosy)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d d
x*sin(y(x)) + --(y(x))*cos(y(x)) + sin(y(x))*y(x) + x*--(y(x))*sin(y(x)) = 0
dx dx
$$x \sin{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + x \sin{\left(y{\left(x \right)} \right)} + y{\left(x \right)} \sin{\left(y{\left(x \right)} \right)} + \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x*sin(y)*y' + x*sin(y) + y*sin(y) + cos(y)*y' = 0
Respuesta
[src]
2 x -- + x*y(x) + log(sin(y(x))) = C1 2
$$\frac{x^{2}}{2} + x y{\left(x \right)} + \log{\left(\sin{\left(y{\left(x \right)} \right)} \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.10459246814679288)
(-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, 7.566503212566957e-67)
(7.777777777777779, 8.388243571811508e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)