Sr Examen
Ecuación diferencial dx*(2*x*y^2+x)+dy*(-x^2*y+3*y)=0
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Solución
Ha introducido
[src]
2 d 2 d
x + 2*x*y (x) + 3*--(y(x))*y(x) - x *--(y(x))*y(x) = 0
dx dx
$$- x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x y^{2}{\left(x \right)} + x + 3 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-x^2*y*y' + 2*x*y^2 + x + 3*y*y' = 0
Respuesta
[src]
_____________________________
___ / 4 2
-\/ 2 *\/ -1 + 9*C1 + C1*x - 6*C1*x
y(x) = ----------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{C_{1} x^{4} - 6 C_{1} x^{2} + 9 C_{1} - 1}}{2}$$
_____________________________
___ / 4 2
\/ 2 *\/ -1 + 9*C1 + C1*x - 6*C1*x
y(x) = --------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{C_{1} x^{4} - 6 C_{1} x^{2} + 9 C_{1} - 1}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -8.781741897946755e-10)
(-5.555555555555555, 6.92837689981384e-310)
(-3.333333333333333, 6.9283778356801e-310)
(-1.1111111111111107, 6.92837689981384e-310)
(1.1111111111111107, 6.92837689981384e-310)
(3.333333333333334, 6.92837689981384e-310)
(5.555555555555557, 6.92837707992567e-310)
(7.777777777777779, 6.92837785455104e-310)
(10.0, 6.92837785455104e-310)
(10.0, 6.92837785455104e-310)