Sr Examen
Ecuación diferencial 4xdx-3ydy=3(x^2)ydy+2x(y^2)dx
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Solución
Ha introducido
[src]
d 2 2 d
4*x - 3*--(y(x))*y(x) = 2*x*y (x) + 3*x *--(y(x))*y(x)
dx dx
$$4 x - 3 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 3 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x y^{2}{\left(x \right)}$$
4*x - 3*y*y' = 3*x^2*y*y' + 2*x*y^2
Respuesta
[src]
_________________
/ C1
y(x) = - / 2 + -----------
/ 2/3
/ / 2\
\/ \1 + x /
$$y{\left(x \right)} = - \sqrt{\frac{C_{1}}{\left(x^{2} + 1\right)^{\frac{2}{3}}} + 2}$$
_________________
/ C1
y(x) = / 2 + -----------
/ 2/3
/ / 2\
\/ \1 + x /
$$y{\left(x \right)} = \sqrt{\frac{C_{1}}{\left(x^{2} + 1\right)^{\frac{2}{3}}} + 2}$$
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, -3.0810955204375094e-09)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 4.958783545387881e-62)
(7.777777777777779, 8.388243571809208e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)