Sr Examen
Ecuación diferencial xdx−ydy=x^2ydy−xy^2dx
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2 d
x - --(y(x))*y(x) = - x*y (x) + x *--(y(x))*y(x)
dx dx
$$x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - x y^{2}{\left(x \right)}$$
x - y*y' = x^2*y*y' - x*y^2
Respuesta
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_________________
/ 2
y(x) = -\/ -1 + C1 + C1*x
$$y{\left(x \right)} = - \sqrt{C_{1} x^{2} + C_{1} - 1}$$
_________________
/ 2
y(x) = \/ -1 + C1 + C1*x
$$y{\left(x \right)} = \sqrt{C_{1} x^{2} + C_{1} - 1}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -3.61672095596209e-10)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 1.1171272167260109e+165)
(7.777777777777779, 8.388243567735593e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)