Sr Examen
Ecuación diferencial dx*(x+2)*(y^2-1)=dy*x^2*y
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 2 d
-2 - x + 2*y (x) + x*y (x) = x *--(y(x))*y(x)
dx
$$x y^{2}{\left(x \right)} - x + 2 y^{2}{\left(x \right)} - 2 = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
x*y^2 - x + 2*y^2 - 2 = x^2*y*y'
Respuesta
[src]
________________
/ -4
/ ---
/ 2 x
y(x) = -\/ 1 + C1*x *e
$$y{\left(x \right)} = - \sqrt{C_{1} x^{2} e^{- \frac{4}{x}} + 1}$$
________________
/ -4
/ ---
/ 2 x
y(x) = \/ 1 + C1*x *e
$$y{\left(x \right)} = \sqrt{C_{1} x^{2} e^{- \frac{4}{x}} + 1}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
almost linear
lie group
separable Integral
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8386276980861832)
(-5.555555555555555, 0.9022445282276073)
(-3.333333333333333, 0.9443589403722217)
(-1.1111111111111107, 0.9313929997492961)
(1.1111111111111107, 4.25268817749816e-09)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 7.566503212566957e-67)
(7.777777777777779, 8.388243567719983e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)