Sr Examen
Ecuación diferencial (x^2+y^2-5)dx+(y+xy)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d d
-5 + x + y (x) + --(y(x))*y(x) + x*--(y(x))*y(x) = 0
dx dx
$$x^{2} + x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y^{2}{\left(x \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 5 = 0$$
x^2 + x*y*y' + y^2 + y*y' - 5 = 0
Respuesta
[src]
_____________________________________
/ 3 4 2
\/ C1 - 24*x - 18*x + 180*x + 360*x
y(x) = ----------------------------------------
6*(1 + x)
$$y{\left(x \right)} = \frac{\sqrt{C_{1} - 18 x^{4} - 24 x^{3} + 180 x^{2} + 360 x}}{6 \left(x + 1\right)}$$
_____________________________________
/ 3 4 2
-\/ C1 - 24*x - 18*x + 180*x + 360*x
y(x) = ------------------------------------------
6*(1 + x)
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} - 18 x^{4} - 24 x^{3} + 180 x^{2} + 360 x}}{6 \left(x + 1\right)}$$
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, 7.6486980486387495)
(-5.555555555555555, 13.380657799504773)
(-3.333333333333333, 26.98326758180791)
(-1.1111111111111107, 567.3652682820746)
(1.1111111111111107, 16542411757291.928)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 4.3149409499051355e-61)
(7.777777777777779, 8.388243566956394e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)