Sr Examen
Ecuación diferencial (y-1)dx+xdy=(y-1)cosydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d d
-1 + x*--(y(x)) + y(x) = - --(y(x))*cos(y(x)) + --(y(x))*cos(y(x))*y(x)
dx dx dx
$$x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} - 1 = y{\left(x \right)} \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} - \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)}$$
x*y' + y - 1 = y*cos(y)*y' - cos(y)*y'
Respuesta
[src]
-cos(y(x)) + x*(-1 + y(x)) - sin(y(x))*y(x) + sin(y(x)) = C1
$$x \left(y{\left(x \right)} - 1\right) - y{\left(x \right)} \sin{\left(y{\left(x \right)} \right)} + \sin{\left(y{\left(x \right)} \right)} - \cos{\left(y{\left(x \right)} \right)} = C_{1}$$
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, 0.6765204677661266)
(-5.555555555555555, 0.5391526738892752)
(-3.333333333333333, 0.1631434300956267)
(-1.1111111111111107, -2.3199368236324256)
(1.1111111111111107, -4.592745087022546)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 2.125757255287192e+160)
(7.777777777777779, 8.388243566958626e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)