Sr Examen
Ecuación diferencial (8xy^2-6/x-9y^2)dx+(4x^2y-6xy)dy=0
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Solución
Ha introducido
[src]
2 6 2 d 2 d
- 9*y (x) - - + 8*x*y (x) - 6*x*--(y(x))*y(x) + 4*x *--(y(x))*y(x) = 0
x dx dx
$$4 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 8 x y^{2}{\left(x \right)} - 6 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 9 y^{2}{\left(x \right)} - \frac{6}{x} = 0$$
4*x^2*y*y' + 8*x*y^2 - 6*x*y*y' - 9*y^2 - 6/x = 0
Respuesta
[src]
______________
/ C1
/ 3 + --
/ 2
/ x
y(x) = - / ------------
\/ x*(-3 + 2*x)
$$y{\left(x \right)} = - \sqrt{\frac{\frac{C_{1}}{x^{2}} + 3}{x \left(2 x - 3\right)}}$$
______________
/ C1
/ 3 + --
/ 2
/ x
y(x) = / ------------
\/ x*(-3 + 2*x)
$$y{\left(x \right)} = \sqrt{\frac{\frac{C_{1}}{x^{2}} + 3}{x \left(2 x - 3\right)}}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
Bernoulli
lie group
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.211731858332049)
(-5.555555555555555, 2.2937391098254505)
(-3.333333333333333, 5.94903149375546)
(-1.1111111111111107, 42.007865099644015)
(1.1111111111111107, 19339605913756.65)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 1.7373559329555976e-47)
(7.777777777777779, 8.388243567339302e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)