Sr Examen
Ecuación diferencial dx*(x*y^3+x)*y+dy*(x^2*y^2-y^2)=0
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Solución
Ha introducido
[src]
4 2 d 2 2 d
x*y (x) + x*y(x) - y (x)*--(y(x)) + x *y (x)*--(y(x)) = 0
dx dx
$$x^{2} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{4}{\left(x \right)} + x y{\left(x \right)} - y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y^2*y' + x*y^4 + x*y - y^2*y' = 0
Respuesta
[src]
y(x) = 0
$$y{\left(x \right)} = 0$$
/ ___ \
___ |\/ 3 *(-1 + 2*y(x))|
/ 2\ / 2 \ \/ 3 *atan|-------------------|
log\-1 + x / log(1 + y(x)) log\1 + y (x) - y(x)/ \ 3 /
------------ - ------------- + --------------------- + ------------------------------- = C1
2 3 6 3
$$\frac{\log{\left(x^{2} - 1 \right)}}{2} - \frac{\log{\left(y{\left(x \right)} + 1 \right)}}{3} + \frac{\log{\left(y^{2}{\left(x \right)} - y{\left(x \right)} + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 y{\left(x \right)} - 1\right)}{3} \right)}}{3} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.2706099232799728)
(-5.555555555555555, 2.6941807498018577)
(-3.333333333333333, 14397894.188611895)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 9.144805860439919e-71)
(7.777777777777779, 8.38824356771842e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)