Sr Examen
Ecuación diferencial y+y'*(lny)^2+y=(x+2lny)y'
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d d
2*y(x) + log (y(x))*--(y(x)) = (x + 2*log(y(x)))*--(y(x))
dx dx
$$2 y{\left(x \right)} + \log{\left(y{\left(x \right)} \right)}^{2} \frac{d}{d x} y{\left(x \right)} = \left(x + 2 \log{\left(y{\left(x \right)} \right)}\right) \frac{d}{d x} y{\left(x \right)}$$
2*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, 0.4842169853069634)
(-5.555555555555555, 0.30350310159817684)
(-3.333333333333333, 0.1888496434971771)
(-1.1111111111111107, 0.11910882797533597)
(1.1111111111111107, 0.07709956818571806)
(3.333333333333334, 0.051436677654382854)
(5.555555555555557, 0.035344627663384864)
(7.777777777777779, 0.02494785204807072)
(10.0, 0.01803065036689695)
(10.0, 0.01803065036689695)