Sr Examen
Ecuación diferencial dx*(2*x*y+y^2)+dy*(x^2+2*x*y-y)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d d d
y (x) + x *--(y(x)) - --(y(x))*y(x) + 2*x*y(x) + 2*x*--(y(x))*y(x) = 0
dx dx dx
$$x^{2} \frac{d}{d x} y{\left(x \right)} + 2 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x y{\left(x \right)} + y^{2}{\left(x \right)} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y' + 2*x*y*y' + 2*x*y + y^2 - y*y' = 0
Respuesta
[src]
____________________
/ 4 2
\/ x - 2*C1 + 4*C1*x - x
y(x) = ----------------------------
-1 + 2*x
$$y{\left(x \right)} = \frac{- x^{2} + \sqrt{4 C_{1} x - 2 C_{1} + x^{4}}}{2 x - 1}$$
/ ____________________\
| 2 / 4 |
-\x + \/ x - 2*C1 + 4*C1*x /
y(x) = --------------------------------
-1 + 2*x
$$y{\left(x \right)} = - \frac{x^{2} + \sqrt{4 C_{1} x - 2 C_{1} + x^{4}}}{2 x - 1}$$
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, 1.416861623141421)
(-5.555555555555555, 3.103715741169466)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 9.144805860439919e-71)
(7.777777777777779, 8.388243567339238e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)