Sr Examen
Ecuación diferencial dx*(x+x*y)+dy*(x^2*y^2+x^2+y^2+1)=0
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Solución
Ha introducido
[src]
2 d 2 d 2 2 d d
x + x*y(x) + x *--(y(x)) + y (x)*--(y(x)) + x *y (x)*--(y(x)) + --(y(x)) = 0
dx dx dx dx
$$x^{2} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x^{2} \frac{d}{d x} y{\left(x \right)} + x y{\left(x \right)} + x + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y^2*y' + x^2*y' + x*y + x + y^2*y' + y' = 0
Respuesta
[src]
2 / 2\ y (x) log\1 + x / ----- + ----------- - y(x) + 2*log(1 + y(x)) = C1 2 2
$$\frac{y^{2}{\left(x \right)}}{2} - y{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + 2 \log{\left(y{\left(x \right)} + 1 \right)} = C_{1}$$
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, 1.012241521583564)
(-5.555555555555555, 1.3140400520802646)
(-3.333333333333333, 1.6857037534667094)
(-1.1111111111111107, 2.2053174693403044)
(1.1111111111111107, 2.2053177695247426)
(3.333333333333334, 1.6857036631760025)
(5.555555555555557, 1.3140400458302355)
(7.777777777777779, 1.0122415751034377)
(10.0, 0.7500001500590194)
(10.0, 0.7500001500590194)