Sr Examen
Ecuación diferencial xdx-2ydy=4xy(xdy-ydx)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2 d
x - 2*--(y(x))*y(x) = - 4*x*y (x) + 4*x *--(y(x))*y(x)
dx dx
$$x - 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 4 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 4 x y^{2}{\left(x \right)}$$
x - 2*y*y' = 4*x^2*y*y' - 4*x*y^2
Respuesta
[src]
___________________
/ 2
-\/ -1 + C1 + 2*C1*x
y(x) = ------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2 C_{1} x^{2} + C_{1} - 1}}{2}$$
___________________
/ 2
\/ -1 + C1 + 2*C1*x
y(x) = ----------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2 C_{1} x^{2} + C_{1} - 1}}{2}$$
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, 0.49306105594920724)
(-5.555555555555555, 0.059716219015132785)
(-3.333333333333333, -6.453993190831599e-09)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 6.397106897951207e+170)
(7.777777777777779, 8.388243567717685e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)