Sr Examen
Ecuación diferencial dy/dx+(((x^3)*((y-1)^3))/((x+1)*y))=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
3 3 x *(-1 + y(x)) d --------------- + --(y(x)) = 0 (1 + x)*y(x) dx
$$\frac{x^{3} \left(y{\left(x \right)} - 1\right)^{3}}{\left(x + 1\right) y{\left(x \right)}} + \frac{d}{d x} y{\left(x \right)} = 0$$
x^3*(y - 1)^3/((x + 1)*y) + y' = 0
Respuesta
[src]
___________________________________________
3 2 ___ / 2 3
-3 + C1 - 6*x - 2*x + 3*x + 6*log(1 + x) - \/ 3 *\/ 3 - C1 - 6*log(1 + x) - 3*x + 2*x + 6*x
y(x) = -------------------------------------------------------------------------------------------------
3 2
C1 - 6*x - 2*x + 3*x + 6*log(1 + x)
$$y{\left(x \right)} = \frac{C_{1} - 2 x^{3} + 3 x^{2} - 6 x - \sqrt{3} \sqrt{- C_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log{\left(x + 1 \right)} + 3} + 6 \log{\left(x + 1 \right)} - 3}{C_{1} - 2 x^{3} + 3 x^{2} - 6 x + 6 \log{\left(x + 1 \right)}}$$
___________________________________________
3 2 ___ / 2 3
-3 + C1 - 6*x - 2*x + 3*x + 6*log(1 + x) + \/ 3 *\/ 3 - C1 - 6*log(1 + x) - 3*x + 2*x + 6*x
y(x) = -------------------------------------------------------------------------------------------------
3 2
C1 - 6*x - 2*x + 3*x + 6*log(1 + x)
$$y{\left(x \right)} = \frac{C_{1} - 2 x^{3} + 3 x^{2} - 6 x + \sqrt{3} \sqrt{- C_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log{\left(x + 1 \right)} + 3} + 6 \log{\left(x + 1 \right)} - 3}{C_{1} - 2 x^{3} + 3 x^{2} - 6 x + 6 \log{\left(x + 1 \right)}}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(0.0, 0.75)
(0.5555555555555556, 0.7503442605266237)
(1.1111111111111112, 0.7541307434731002)
(1.6666666666666667, 0.7657024955149159)
(2.2222222222222223, 0.7859490896565816)
(2.7777777777777777, 0.8112388434974784)
(3.3333333333333335, 0.8368609932944386)
(3.8888888888888893, 0.8599276322573883)
(4.444444444444445, 0.8795024575372079)
(5.0, 0.8957004739439215)
(5.0, 0.8957004739439215)