Sr Examen
Ecuación diferencial (1+sin^2(x))*y'=(cos(x))*(y+(1+sin^2))*(e^(arctan(sen(x))))
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Solución
Ha introducido
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/ 2 \ d / 2 \ atan(sin(x))
\1 + sin (x)/*--(y(x)) = \1 + sin (x) + y(x)/*cos(x)*e
dx
$$\left(\sin^{2}{\left(x \right)} + 1\right) \frac{d}{d x} y{\left(x \right)} = \left(y{\left(x \right)} + \sin^{2}{\left(x \right)} + 1\right) e^{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}} \cos{\left(x \right)}$$
(sin(x)^2 + 1)*y' = (y + sin(x)^2 + 1)*exp(atan(sin(x)))*cos(x)
Gráfico para el problema de Cauchy
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, -0.5974824331204859)
(-5.555555555555555, 1.0986485659586742)
(-3.333333333333333, 0.07974492675843131)
(-1.1111111111111107, -0.5646810945708894)
(1.1111111111111107, 1.9649309650907842)
(3.333333333333334, -0.26451764204927425)
(5.555555555555557, -0.4842449621683866)
(7.777777777777779, 2.428994169189502)
(10.0, -0.4376443325990704)
(10.0, -0.4376443325990704)