Sr Examen
Ecuación diferencial ((sin(x+y)+sin(x-y))dx+dy)/cos(y)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d --(y(x)) dx sin(x - y(x)) sin(x + y(x)) --------- + ------------- + ------------- = 0 cos(y(x)) cos(y(x)) cos(y(x))
$$\frac{\sin{\left(x - y{\left(x \right)} \right)}}{\cos{\left(y{\left(x \right)} \right)}} + \frac{\sin{\left(x + y{\left(x \right)} \right)}}{\cos{\left(y{\left(x \right)} \right)}} + \frac{\frac{d}{d x} y{\left(x \right)}}{\cos{\left(y{\left(x \right)} \right)}} = 0$$
sin(x - y)/cos(y) + sin(x + y)/cos(y) + y'/cos(y) = 0
Respuesta
[src]
/ 1 \
y(x) = pi - asin|-------------------|
\tanh(C1 + 2*cos(x))/
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(\frac{1}{\tanh{\left(C_{1} + 2 \cos{\left(x \right)} \right)}} \right)}$$
/ 1 \
y(x) = asin|-------------------|
\tanh(C1 + 2*cos(x))/
$$y{\left(x \right)} = \operatorname{asin}{\left(\frac{1}{\tanh{\left(C_{1} + 2 \cos{\left(x \right)} \right)}} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
almost linear
1st power series
lie group
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.4314850278931959)
(-5.555555555555555, 1.5343087295887718)
(-3.333333333333333, 0.5215713711807735)
(-1.1111111111111107, 1.5039174611432011)
(1.1111111111111107, 1.503917514783346)
(3.333333333333334, 0.521573846384684)
(5.555555555555557, 1.5343088316015023)
(7.777777777777779, 1.4314851373944135)
(10.0, 0.750000798938551)
(10.0, 0.750000798938551)