Sr Examen
Ecuación diferencial dx*(1/x+y/x^2)=dy*(y+1/x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d
--(y(x))
1 y(x) dx d
- + ---- = -------- + --(y(x))*y(x)
x 2 x dx
x
$$\frac{1}{x} + \frac{y{\left(x \right)}}{x^{2}} = y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{\frac{d}{d x} y{\left(x \right)}}{x}$$
1/x + y/x^2 = y*y' + y'/x
Respuesta
[src]
_________________________
/ 2 2
-1 + \/ 1 + C1*x + 2*x *log(x)
y(x) = ---------------------------------
x
$$y{\left(x \right)} = \frac{\sqrt{C_{1} x^{2} + 2 x^{2} \log{\left(x \right)} + 1} - 1}{x}$$
_________________________
/ 2 2
-1 - \/ 1 + C1*x + 2*x *log(x)
y(x) = ---------------------------------
x
$$y{\left(x \right)} = \frac{- \sqrt{C_{1} x^{2} + 2 x^{2} \log{\left(x \right)} + 1} - 1}{x}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.12385229086921372)
(-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, 6.016175465029022e-67)
(7.777777777777779, 8.388243566956694e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)