Sr Examen
Ecuación diferencial tg(x)*sin(y)^2*dx+cos(x)^2*ctg(xy)*dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d
sin (y(x))*tan(x) + cos (x)*--(y(x))*cot(x*y(x)) = 0
dx
$$\sin^{2}{\left(y{\left(x \right)} \right)} \tan{\left(x \right)} + \cos^{2}{\left(x \right)} \cot{\left(x y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
sin(y)^2*tan(x) + cos(x)^2*cot(x*y)*y' = 0
Respuesta
[src]
3 2 5 2 / 2\
C1*x *sin (C1) C1*x *sin (C1)*\-4 - C1 / / 6\
y(x) = C1 - -------------- + ------------------------- + O\x /
3 15
$$y{\left(x \right)} = C_{1} - \frac{C_{1} x^{3} \sin^{2}{\left(C_{1} \right)}}{3} + \frac{C_{1} x^{5} \left(- C_{1}^{2} - 4\right) \sin^{2}{\left(C_{1} \right)}}{15} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.5438160836295345)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 7.793670397367311e-43)
(7.777777777777779, 8.388243567356035e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)