Sr Examen
Ecuación diferencial (2xy^2+3y^3)/(y^2)dx-(7-3xy^2)/(y^2)dy=0
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Solución
Ha introducido
[src]
d
7*--(y(x))
dx d
2*x + 3*y(x) - ---------- + 3*x*--(y(x)) = 0
2 dx
y (x)
$$3 x \frac{d}{d x} y{\left(x \right)} + 2 x + 3 y{\left(x \right)} - \frac{7 \frac{d}{d x} y{\left(x \right)}}{y^{2}{\left(x \right)}} = 0$$
3*x*y' + 2*x + 3*y - 7*y'/y^2 = 0
Respuesta
[src]
___________________________
/ 2 4 2
x \/ C1 + x - 84*x - 2*C1*x C1
y(x) = - - - ------------------------------ + ---
6 6*x 6*x
$$y{\left(x \right)} = \frac{C_{1}}{6 x} - \frac{x}{6} - \frac{\sqrt{C_{1}^{2} - 2 C_{1} x^{2} + x^{4} - 84 x}}{6 x}$$
___________________________
/ 2 4 2
x C1 \/ C1 + x - 84*x - 2*C1*x
y(x) = - - + --- + ------------------------------
6 6*x 6*x
$$y{\left(x \right)} = \frac{C_{1}}{6 x} - \frac{x}{6} + \frac{\sqrt{C_{1}^{2} - 2 C_{1} x^{2} + x^{4} - 84 x}}{6 x}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.22207275520565897)
(-5.555555555555555, 0.12072860672618416)
(-3.333333333333333, 0.09134129356854653)
(-1.1111111111111107, 0.08151807782881548)
(1.1111111111111107, 0.082038938886198)
(3.333333333333334, 0.09360013804890639)
(5.555555555555557, 0.13011012984383544)
(7.777777777777779, 0.4281619141676823)
(10.0, 0.5461385567971173)
(10.0, 0.5461385567971173)