Sr Examen
Ecuación diferencial (x+x*y^2)*dx+(1+x^4)*arctg(y)*dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d 4 d
x + x*y (x) + --(y(x))*atan(y(x)) + x *--(y(x))*atan(y(x)) = 0
dx dx
$$x^{4} \operatorname{atan}{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} + x + \operatorname{atan}{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^4*atan(y)*y' + x*y^2 + x + atan(y)*y' = 0
Respuesta
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/ _______________\
| / / 2\ |
y(x) = -tan\\/ C1 - atan\x / /
$$y{\left(x \right)} = - \tan{\left(\sqrt{C_{1} - \operatorname{atan}{\left(x^{2} \right)}} \right)}$$
/ _______________\
| / / 2\ |
y(x) = tan\\/ C1 - atan\x / /
$$y{\left(x \right)} = \tan{\left(\sqrt{C_{1} - \operatorname{atan}{\left(x^{2} \right)}} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st power series
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7579263139523019)
(-5.555555555555555, 0.7771765637150813)
(-3.333333333333333, 0.8469941285342664)
(-1.1111111111111107, 1.7098244466233792)
(1.1111111111111107, 1.7098243880623751)
(3.333333333333334, 0.8469946835065425)
(5.555555555555557, 0.7771773844800566)
(7.777777777777779, 0.7579272373111827)
(10.0, 0.7500009992357065)
(10.0, 0.7500009992357065)