Sr Examen
Ecuación diferencial 6*dx*x+6*dy*y=-3*dx*x*y^2+2*dy*x^2*y
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2 d
6*x + 6*--(y(x))*y(x) = - 3*x*y (x) + 2*x *--(y(x))*y(x)
dx dx
$$6 x + 6 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)}$$
6*x + 6*y*y' = 2*x^2*y*y' - 3*x*y^2
Respuesta
[src]
___________________________________________________
/ _________ _________
/ / 2 2*C1 2 / 2 2*C1
y(x) = -\/ -2 - 3*\/ -3 + x *e + x *\/ -3 + x *e
$$y{\left(x \right)} = - \sqrt{x^{2} \sqrt{x^{2} - 3} e^{2 C_{1}} - 3 \sqrt{x^{2} - 3} e^{2 C_{1}} - 2}$$
___________________________________________________
/ _________ _________
/ / 2 2*C1 2 / 2 2*C1
y(x) = \/ -2 - 3*\/ -3 + x *e + x *\/ -3 + x *e
$$y{\left(x \right)} = \sqrt{x^{2} \sqrt{x^{2} - 3} e^{2 C_{1}} - 3 \sqrt{x^{2} - 3} e^{2 C_{1}} - 2}$$
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, 1.8218789502058455e-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, 2.6509947707452356e-52)
(7.777777777777779, 8.388243567355225e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)