Sr Examen
Ecuación diferencial e^(2*x)(y')-2*x*y-y^2-1=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 d 2*x
-1 - y (x) + --(y(x))*e - 2*x*y(x) = 0
dx
$$- 2 x y{\left(x \right)} - y^{2}{\left(x \right)} + e^{2 x} \frac{d}{d x} y{\left(x \right)} - 1 = 0$$
-2*x*y - y^2 + exp(2*x)*y' - 1 = 0
Respuesta
[src]
3 / 2 / 2\ / 2\ / 2\\ 4 / 2 / 2\ / 2\ / 2 \ / 2\ / 2 / 2\ / 2\ \ / 2\ / 2\ / 2\\ 5 / 2 / 2\ / 2 / 2\ / 2\ / 2\ / 2 \\ / 2\ / 2 / 2\ / 2\ / 2 \ / 2 / 2\ / 2\ \ / 2\ / 2 \ / 2\ \ / 2\ / 2\ / 2\ / 2 \ / 2\ / 2 / 2\ / 2\ \ / 2\ / 2\ / 2 / 2\ / 2\ \ / 2\ / 2 \ / 2 \ / 2\ / 2\\
/ 2\ 2 / 2 / 2\\ x *\3 - 4*C1 + 5*C1 + \1 + C1 /*\2 - 2*C1 + 3*C1 / - 4*C1*\1 + C1 // x *\-6 - 14*C1 + 8*C1 + C1*\2 - 2*C1 + 3*C1 / + \1 + C1 /*\-4 - 6*C1 + 5*C1/ + \1 + C1 /*\-4 - 6*C1 + 5*C1 + C1*\2 - 2*C1 + 3*C1 / + \1 + C1 /*(-1 + 3*C1)/ - \1 + C1 /*\2 - 2*C1 + 3*C1 / + 8*C1*\1 + C1 // x *\28 - 40*C1 + 76*C1 + \1 + C1 /*\18 - 30*C1 + 27*C1 + \1 + C1 /*(5 - 12*C1) - 2*C1*\2 - 2*C1 + 3*C1 / - 2*\1 + C1 /*(-1 + 3*C1) + 2*C1*(-1 + 3*C1) + 2*C1*\-4 - 6*C1 + 5*C1// + \1 + C1 /*\18 - 30*C1 + 27*C1 + \1 + C1 /*(5 - 12*C1) - 2*C1*\2 - 2*C1 + 3*C1 / + 2*C1*(-1 + 3*C1) + 2*C1*\-4 - 6*C1 + 5*C1/ + 2*C1*\-4 - 6*C1 + 5*C1 + C1*\2 - 2*C1 + 3*C1 / + \1 + C1 /*(-1 + 3*C1)/ + 2*\1 + C1 /*\5 - 7*C1 + 3*C1 + 2*C1*(-1 + 3*C1)/ + 2*\-1 - C1 /*(-1 + 3*C1)/ - 32*C1*\1 + C1 / - 4*C1*\2 - 2*C1 + 3*C1 / - 2*\1 + C1 /*\-4 - 6*C1 + 5*C1/ - 2*\1 + C1 /*\-4 - 6*C1 + 5*C1 + C1*\2 - 2*C1 + 3*C1 / + \1 + C1 /*(-1 + 3*C1)/ - 2*\-1 - C1 /*\2 - 2*C1 + 3*C1 / + 2*C1*\-4 - 6*C1 + 5*C1 + C1*\2 - 2*C1 + 3*C1 / + \1 + C1 /*(-1 + 3*C1)/ + 2*\-1 - C1 /*\-4 - 6*C1 + 5*C1/ + 4*C1*\-4 - 6*C1 + 5*C1/ + 4*\1 + C1 /*\4 - 7*C1 + 6*C1 // / 6\
y(x) = C1 + x*\1 + C1 / + x *\-1 + C1 - C1 + C1*\1 + C1 // + --------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + O\x /
3 6 30
$$y{\left(x \right)} = x \left(C_{1}^{2} + 1\right) + x^{2} \left(- C_{1}^{2} + C_{1} \left(C_{1}^{2} + 1\right) + C_{1} - 1\right) + \frac{x^{3} \left(5 C_{1}^{2} - 4 C_{1} \left(C_{1}^{2} + 1\right) - 4 C_{1} + \left(C_{1}^{2} + 1\right) \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 3\right)}{3} + \frac{x^{4} \left(- 14 C_{1}^{2} + 8 C_{1} \left(C_{1}^{2} + 1\right) + C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 8 C_{1} + \left(C_{1}^{2} + 1\right) \left(- 6 C_{1}^{2} + 5 C_{1} - 4\right) - \left(C_{1}^{2} + 1\right) \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + \left(C_{1}^{2} + 1\right) \left(- 6 C_{1}^{2} + C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 5 C_{1} + \left(3 C_{1} - 1\right) \left(C_{1}^{2} + 1\right) - 4\right) - 6\right)}{6} + \frac{x^{5} \left(76 C_{1}^{2} - 32 C_{1} \left(C_{1}^{2} + 1\right) + 4 C_{1} \left(- 6 C_{1}^{2} + 5 C_{1} - 4\right) - 4 C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 2 C_{1} \left(- 6 C_{1}^{2} + C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 5 C_{1} + \left(3 C_{1} - 1\right) \left(C_{1}^{2} + 1\right) - 4\right) - 40 C_{1} + 2 \left(- C_{1}^{2} - 1\right) \left(- 6 C_{1}^{2} + 5 C_{1} - 4\right) - 2 \left(- C_{1}^{2} - 1\right) \left(3 C_{1}^{2} - 2 C_{1} + 2\right) - 2 \left(C_{1}^{2} + 1\right) \left(- 6 C_{1}^{2} + 5 C_{1} - 4\right) + 4 \left(C_{1}^{2} + 1\right) \left(6 C_{1}^{2} - 7 C_{1} + 4\right) - 2 \left(C_{1}^{2} + 1\right) \left(- 6 C_{1}^{2} + C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 5 C_{1} + \left(3 C_{1} - 1\right) \left(C_{1}^{2} + 1\right) - 4\right) + \left(C_{1}^{2} + 1\right) \left(27 C_{1}^{2} + 2 C_{1} \left(3 C_{1} - 1\right) + 2 C_{1} \left(- 6 C_{1}^{2} + 5 C_{1} - 4\right) - 2 C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) - 30 C_{1} + \left(5 - 12 C_{1}\right) \left(C_{1}^{2} + 1\right) - 2 \left(3 C_{1} - 1\right) \left(C_{1}^{2} + 1\right) + 18\right) + \left(C_{1}^{2} + 1\right) \left(27 C_{1}^{2} + 2 C_{1} \left(3 C_{1} - 1\right) + 2 C_{1} \left(- 6 C_{1}^{2} + 5 C_{1} - 4\right) - 2 C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 2 C_{1} \left(- 6 C_{1}^{2} + C_{1} \left(3 C_{1}^{2} - 2 C_{1} + 2\right) + 5 C_{1} + \left(3 C_{1} - 1\right) \left(C_{1}^{2} + 1\right) - 4\right) - 30 C_{1} + \left(5 - 12 C_{1}\right) \left(C_{1}^{2} + 1\right) + 2 \left(3 C_{1} - 1\right) \left(- C_{1}^{2} - 1\right) + 2 \left(C_{1}^{2} + 1\right) \left(3 C_{1}^{2} + 2 C_{1} \left(3 C_{1} - 1\right) - 7 C_{1} + 5\right) + 18\right) + 28\right)}{30} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.06455360592884644)
(-5.555555555555555, 0.09074103583955279)
(-3.333333333333333, 0.15352634845811236)
(-1.1111111111111107, 0.5547788525499235)
(1.1111111111111107, 1143369.202200472)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 9.836995015458208e-72)
(7.777777777777779, 8.388243567719906e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)