Sr Examen
Ecuación diferencial (sin(y)+y*sin(x)+(1/x))dx+(x*cosy-cosx+(1/y))dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d
--(y(x))
1 dx d d
- + -------- + sin(x)*y(x) - --(y(x))*cos(x) + x*--(y(x))*cos(y(x)) + sin(y(x)) = 0
x y(x) dx dx
$$x \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \sin{\left(x \right)} + \sin{\left(y{\left(x \right)} \right)} - \cos{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{\frac{d}{d x} y{\left(x \right)}}{y{\left(x \right)}} + \frac{1}{x} = 0$$
x*cos(y)*y' + y*sin(x) + sin(y) - cos(x)*y' + y'/y + 1/x = 0
Respuesta
[src]
x*sin(y(x)) - cos(x)*y(x) + log(x) + log(y(x)) = C1
$$x \sin{\left(y{\left(x \right)} \right)} - y{\left(x \right)} \cos{\left(x \right)} + \log{\left(x \right)} + \log{\left(y{\left(x \right)} \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8887719431393374)
(-5.555555555555555, 1.1975176514162678)
(-3.333333333333333, 1.5636697584806218)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 5.107659831618641e-38)
(7.777777777777779, 8.388243571828904e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)