Sr Examen
Ecuación diferencial y-y'(lny)^2=(x+2lny)y'
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d d
- log (y(x))*--(y(x)) + y(x) = (x + 2*log(y(x)))*--(y(x))
dx dx
$$y{\left(x \right)} - \log{\left(y{\left(x \right)} \right)}^{2} \frac{d}{d x} y{\left(x \right)} = \left(x + 2 \log{\left(y{\left(x \right)} \right)}\right) \frac{d}{d x} y{\left(x \right)}$$
y - log(y)^2*y' = (x + 2*log(y))*y'
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.5934543059265377)
(-5.555555555555555, 0.44128038681169884)
(-3.333333333333333, 0.2913312725819904)
(-1.1111111111111107, 0.11512720676112632)
(1.1111111111111107, 0.08898435006037766)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 1.7373559329555976e-47)
(7.777777777777779, 8.388243567717308e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)