Sr Examen
Ecuación diferencial 2xy^(2)dx-ydy=yx^(2)dy-6xdx
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d 2 2 d - --(y(x))*y(x) + 2*x*y (x) = -6*x + x *--(y(x))*y(x) dx dx
$$2 x y^{2}{\left(x \right)} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 6 x$$
2*x*y^2 - y*y' = x^2*y*y' - 6*x
Respuesta
[src]
___________________________
/ 4 2
y(x) = -\/ -3 + C1 + C1*x + 2*C1*x
$$y{\left(x \right)} = - \sqrt{C_{1} x^{4} + 2 C_{1} x^{2} + C_{1} - 3}$$
___________________________
/ 4 2
y(x) = \/ -3 + C1 + C1*x + 2*C1*x
$$y{\left(x \right)} = \sqrt{C_{1} x^{4} + 2 C_{1} x^{2} + C_{1} - 3}$$
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, 1.0658963162428414e-09)
(-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)