Sr Examen
Ecuación diferencial ylnydx+(x-lny)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d x*--(y(x)) + log(y(x))*y(x) - --(y(x))*log(y(x)) = 0 dx dx
$$x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \log{\left(y{\left(x \right)} \right)} - \log{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x*y' + y*log(y) - log(y)*y' = 0
Respuesta
[src]
_________
/ 2
x - \/ C1 + x
y(x) = e
$$y{\left(x \right)} = e^{x - \sqrt{C_{1} + x^{2}}}$$
_________
/ 2
x + \/ C1 + x
y(x) = e
$$y{\left(x \right)} = e^{x + \sqrt{C_{1} + x^{2}}}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.6883031397458659)
(-5.555555555555555, 0.5849310128873467)
(-3.333333333333333, 0.3675468467526112)
(-1.1111111111111107, 0.09242446220500161)
(1.1111111111111107, 6.95183464577476e-310)
(3.333333333333334, 6.9518346457811e-310)
(5.555555555555557, 6.95183464716604e-310)
(7.777777777777779, 6.9520529151772e-310)
(10.0, 6.9518346420404e-310)
(10.0, 6.9518346420404e-310)