Sr Examen
Ecuación diferencial (1-x^(2)*y)*dx+x^(2)(y-x)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 3 d 2 d
1 - x *y(x) - x *--(y(x)) + x *--(y(x))*y(x) = 0
dx dx
$$- x^{3} \frac{d}{d x} y{\left(x \right)} + x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - x^{2} y{\left(x \right)} + 1 = 0$$
-x^3*y' + x^2*y*y' - x^2*y + 1 = 0
Respuesta
[src]
___________________
2 / / 3 \
x - \/ x*\2 + x + C1*x/
y(x) = ---------------------------
x
$$y{\left(x \right)} = \frac{x^{2} - \sqrt{x \left(C_{1} x + x^{3} + 2\right)}}{x}$$
___________________
2 / / 3 \
x + \/ x*\2 + x + C1*x/
y(x) = ---------------------------
x
$$y{\left(x \right)} = \frac{x^{2} + \sqrt{x \left(C_{1} x + x^{3} + 2\right)}}{x}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.9399733658124052)
(-5.555555555555555, 1.2464072803288881)
(-3.333333333333333, 1.7924456821495962)
(-1.1111111111111107, 2.7872296029333095)
(1.1111111111111107, -0.1267544057879289)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 1.7373559329555976e-47)
(7.777777777777779, 8.388243567719913e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)