Sr Examen
Ecuación diferencial (x^2+y/x)dx+(log(x)+2y)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 y(x) d d
x + ---- + --(y(x))*log(x) + 2*--(y(x))*y(x) = 0
x dx dx
$$x^{2} + 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \log{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{y{\left(x \right)}}{x} = 0$$
x^2 + 2*y*y' + log(x)*y' + y/x = 0
Respuesta
[src]
________________________
/ 3 2
log(x) \/ C1 - 12*x + 9*log (x)
y(x) = - ------ - ---------------------------
2 6
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} - 12 x^{3} + 9 \log{\left(x \right)}^{2}}}{6} - \frac{\log{\left(x \right)}}{2}$$
________________________
/ 3 2
log(x) \/ C1 - 12*x + 9*log (x)
y(x) = - ------ + ---------------------------
2 6
$$y{\left(x \right)} = \frac{\sqrt{C_{1} - 12 x^{3} + 9 \log{\left(x \right)}^{2}}}{6} - \frac{\log{\left(x \right)}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, nan)
(-5.555555555555555, nan)
(-3.333333333333333, nan)
(-1.1111111111111107, nan)
(1.1111111111111107, nan)
(3.333333333333334, nan)
(5.555555555555557, nan)
(7.777777777777779, nan)
(10.0, nan)
(10.0, nan)