Sr Examen
Ecuación diferencial (2x+3xy^2)dx+(3y+3yx^2)dy=0
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Solución
Ha introducido
[src]
2 d 2 d
2*x + 3*x*y (x) + 3*--(y(x))*y(x) + 3*x *--(y(x))*y(x) = 0
dx dx
$$3 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 3 x y^{2}{\left(x \right)} + 2 x + 3 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
3*x^2*y*y' + 3*x*y^2 + 2*x + 3*y*y' = 0
Respuesta
[src]
___________
/ 2
___ / C1 - 2*x
\/ 3 * / ---------
/ 2
\/ 1 + x
y(x) = -----------------------
3
$$y{\left(x \right)} = \frac{\sqrt{3} \sqrt{\frac{C_{1} - 2 x^{2}}{x^{2} + 1}}}{3}$$
___________
/ 2
___ / C1 - 2*x
-\/ 3 * / ---------
/ 2
\/ 1 + x
y(x) = -------------------------
3
$$y{\left(x \right)} = - \frac{\sqrt{3} \sqrt{\frac{C_{1} - 2 x^{2}}{x^{2} + 1}}}{3}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.1628275485577957)
(-5.555555555555555, 1.7970605309215333)
(-3.333333333333333, 3.0957897576650435)
(-1.1111111111111107, 7.408801418930054)
(1.1111111111111107, 7.408801914838975)
(3.333333333333334, 3.0957897047788485)
(5.555555555555557, 1.797060846946645)
(7.777777777777779, 1.1628279224145772)
(10.0, 0.7500005427554473)
(10.0, 0.7500005427554473)