Sr Examen
Ecuación diferencial tgy*ctgx*y'=1
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d --(y(x))*cot(x)*tan(y(x)) = 1 dx
$$\tan{\left(y{\left(x \right)} \right)} \cot{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 1$$
tan(y)*cot(x)*y' = 1
Respuesta
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y(x) = -acos(C1*cos(x)) + 2*pi
$$y{\left(x \right)} = - \operatorname{acos}{\left(C_{1} \cos{\left(x \right)} \right)} + 2 \pi$$
y(x) = acos(C1*cos(x))
$$y{\left(x \right)} = \operatorname{acos}{\left(C_{1} \cos{\left(x \right)} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.6372306756114112)
(-5.555555555555555, 2.27991931480811)
(-3.333333333333333, 0.5432793914685055)
(-1.1111111111111107, 1.9680352711688058)
(1.1111111111111107, 1.9680352843287112)
(3.333333333333334, 0.5431762070390542)
(5.555555555555557, 3.141592653513462)
(7.777777777777779, 8.388243571809208e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)