Sr Examen
Ecuación diferencial y*x^2dy-3x*y^2dx=6xdx-ydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d d
- 3*x*y (x) + x *--(y(x))*y(x) = 6*x - --(y(x))*y(x)
dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)} = 6 x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
x^2*y*y' - 3*x*y^2 = 6*x - y*y'
Respuesta
[src]
_____________________________________
/ 6 2 4
y(x) = -\/ -2 + C1 + C1*x + 3*C1*x + 3*C1*x
$$y{\left(x \right)} = - \sqrt{C_{1} x^{6} + 3 C_{1} x^{4} + 3 C_{1} x^{2} + C_{1} - 2}$$
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/ 6 2 4
y(x) = \/ -2 + C1 + C1*x + 3*C1*x + 3*C1*x
$$y{\left(x \right)} = \sqrt{C_{1} x^{6} + 3 C_{1} x^{4} + 3 C_{1} x^{2} + C_{1} - 2}$$
Gráfico para el problema de Cauchy
Clasificación
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, -6.059737002322734e-10)
(-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, 3.1237768967464496e-33)
(7.777777777777779, 8.388243567719172e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)