Sr Examen
Ecuación diferencial xydx-sqr(x^2+1)*ln^2ydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d 4 2 d 2 2 d
x*y(x) - log (y(x))*--(y(x)) - x *log (y(x))*--(y(x)) - 2*x *log (y(x))*--(y(x)) = 0
dx dx dx
$$- x^{4} \log{\left(y{\left(x \right)} \right)}^{2} \frac{d}{d x} y{\left(x \right)} - 2 x^{2} \log{\left(y{\left(x \right)} \right)}^{2} \frac{d}{d x} y{\left(x \right)} + x y{\left(x \right)} - \log{\left(y{\left(x \right)} \right)}^{2} \frac{d}{d x} y{\left(x \right)} = 0$$
-x^4*log(y)^2*y' - 2*x^2*log(y)^2*y' + x*y - log(y)^2*y' = 0
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st power series
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.724782512580294)
(-5.555555555555555, 0.6820450854433119)
(-3.333333333333333, 0.600372743457247)
(-1.1111111111111107, 0.41500535405994937)
(1.1111111111111107, 0.4150053987884476)
(3.333333333333334, 0.6003737389156047)
(5.555555555555557, 0.682046992708352)
(7.777777777777779, 0.7247853143242073)
(10.0, 0.7500035799319091)
(10.0, 0.7500035799319091)