Sr Examen
Ecuación diferencial siny*x'+cosx*y'=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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d --(y(x))*cos(x) + sin(y(x)) = 0 dx
$$\sin{\left(y{\left(x \right)} \right)} + \cos{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
sin(y) + cos(x)*y' = 0
Respuesta
[src]
/1 - C1 + C1*sin(x) + sin(x)\
y(x) = - acos|---------------------------| + 2*pi
\1 + C1 - C1*sin(x) + sin(x)/
$$y{\left(x \right)} = - \operatorname{acos}{\left(\frac{C_{1} \sin{\left(x \right)} - C_{1} + \sin{\left(x \right)} + 1}{- C_{1} \sin{\left(x \right)} + C_{1} + \sin{\left(x \right)} + 1} \right)} + 2 \pi$$
/1 - C1 + C1*sin(x) + sin(x)\
y(x) = acos|---------------------------|
\1 + C1 - C1*sin(x) + sin(x)/
$$y{\left(x \right)} = \operatorname{acos}{\left(\frac{C_{1} \sin{\left(x \right)} - C_{1} + \sin{\left(x \right)} + 1}{- C_{1} \sin{\left(x \right)} + C_{1} + \sin{\left(x \right)} + 1} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st power series
lie group
separable Integral
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 5.502599290392942)
(-5.555555555555555, 6.26911902290436)
(-3.333333333333333, 6.3090486197400475)
(-1.1111111111111107, 12.432464920384108)
(1.1111111111111107, 12.559029013270173)
(3.333333333333334, 12.60444782909589)
(5.555555555555557, 18.77957401348216)
(7.777777777777779, 18.84835890241297)
(10.0, 18.90728430508191)
(10.0, 18.90728430508191)