Sr Examen
Ecuación diferencial dy*(-2*x^2*y-6*y)=dx*(-3*x*y^2-6*x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 d 2
- 6*--(y(x))*y(x) - 2*x *--(y(x))*y(x) = -6*x - 3*x*y (x)
dx dx
$$- 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 6 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - 3 x y^{2}{\left(x \right)} - 6 x$$
-2*x^2*y*y' - 6*y*y' = -3*x*y^2 - 6*x
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, -3.296743055950872e-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, 2.5910489201161894e+184)
(7.777777777777779, 8.388243567339603e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)