Sr Examen
Ecuación diferencial ydy-(2*y^2)/(x^2)dx=dx/(x^3)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
d 2*y (x) 1
--(y(x))*y(x) - ------- = --
dx 2 3
x x
$$y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - \frac{2 y^{2}{\left(x \right)}}{x^{2}} = \frac{1}{x^{3}}$$
y*y' - 2*y^2/x^2 = x^(-3)
Respuesta
[src]
_________________
/ -4
/ ---
/ 8 x
- / 2 - - + C1*e
\/ x
y(x) = -------------------------
4
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} e^{- \frac{4}{x}} + 2 - \frac{8}{x}}}{4}$$
_________________
/ -4
/ ---
/ 8 x
/ 2 - - + C1*e
\/ x
y(x) = -----------------------
4
$$y{\left(x \right)} = \frac{\sqrt{C_{1} e^{- \frac{4}{x}} + 2 - \frac{8}{x}}}{4}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
Bernoulli
almost linear
lie group
1st exact Integral
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7897476558902049)
(-5.555555555555555, 0.8652383130808439)
(-3.333333333333333, 1.0664887772691474)
(-1.1111111111111107, 3.1751195744111236)
(1.1111111111111107, 6.453812051075744e+26)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 2.125757255287192e+160)
(7.777777777777779, 8.388243566974915e+296)
(10.0, 1.975203368165537e+166)
(10.0, 1.975203368165537e+166)