Sr Examen
Ecuación diferencial dx*(y-1)*y^3+3*dy*x*(y-1)*y^2=dy*(y+2)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
4 3 2 d 3 d d d
y (x) - y (x) - 3*x*y (x)*--(y(x)) + 3*x*y (x)*--(y(x)) = 2*--(y(x)) + --(y(x))*y(x)
dx dx dx dx
$$3 x y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y^{4}{\left(x \right)} - y^{3}{\left(x \right)} = y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)}$$
3*x*y^3*y' - 3*x*y^2*y' + y^4 - y^3 = y*y' + 2*y'
Respuesta
[src]
3 -y(x) - 3*log(-1 + y(x)) + x*y (x) = C1
$$x y^{3}{\left(x \right)} - y{\left(x \right)} - 3 \log{\left(y{\left(x \right)} - 1 \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8597355672005529)
(-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, 8.973398002470273e-67)
(7.777777777777779, 8.388243567736333e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)