Sr Examen
Ecuación diferencial dy/dx-y=y^2(-1-e^3x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d 2 / 3\
-y(x) + --(y(x)) = y (x)*\-1 - x*e /
dx
$$- y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = \left(- x e^{3} - 1\right) y^{2}{\left(x \right)}$$
-y + y' = (-x*exp(3) - 1)*y^2
Respuesta
[src]
2 / 3\ 3 / / 2 2 3\ 3 3\ 4 / / / 2 2 3\ 2 3 3 / 3 \ 3 3\ 2 6 / 2 2 3\ 3 3\ 5 / / / / 2 2 3\ 2 3 3 / 3 \ 3 3\ 2 6 / 2 2 3\ 3 2 / 3 \ 3 / 2 2 / 3 \ 3 3\ 3 3\ / / 2 2 3\ 2 3 3 / 3 \ 3 3\ 3 2 6 2 6 / 2 2 / 3 \ 3\ 3\
C1*x *\(1 - C1)*(1 - 2*C1) - C1*e / C1*x *\(1 - C1)*\(1 - 2*C1) - 2*C1 + 2*C1 - 2*C1*e / - C1*(1 - 2*C1)*e - 2*C1*(1 - C1)*e / C1*x *\(1 - C1)*\(1 - 2*C1)*\(1 - 2*C1) - 2*C1 + 2*C1 - 2*C1*e / + 2*C1 *e - 2*C1*(1 - 2*C1)*e + 2*C1*(1 - C1)*\-3 - e + 6*C1/ + 2*C1*(-1 + C1)*e + 2*C1*(-1 + 2*C1)*e / + 4*C1 *e - C1*\(1 - 2*C1) - 2*C1 + 2*C1 - 2*C1*e /*e + 6*C1*(1 - C1)*(-1 + 2*C1)*e / C1*x *\(1 - C1)*\(1 - 2*C1)*\(1 - 2*C1)*\(1 - 2*C1) - 2*C1 + 2*C1 - 2*C1*e / + 2*C1 *e - 2*C1*(1 - 2*C1)*e + 2*C1*(1 - C1)*\-3 - e + 6*C1/ + 2*C1*(-1 + C1)*e + 2*C1*(-1 + 2*C1)*e / + 12*C1 *e - 2*C1*\(1 - 2*C1) - 2*C1 + 2*C1 - 2*C1*e /*e - 2*C1 *\-3 - e + 6*C1/*e + 2*C1*(1 - C1)*\- (1 - 2*C1) - 8*C1 + 8*C1 + 2*(1 - 2*C1)*\-3 - e + 6*C1/ + 3*(-1 + 2*C1)*e + 8*C1*e / + 6*C1*(1 - C1)*(-1 + 4*C1)*e + 6*C1*(1 - 2*C1)*(-1 + 2*C1)*e / - C1*\(1 - 2*C1)*\(1 - 2*C1) - 2*C1 + 2*C1 - 2*C1*e / + 2*C1 *e - 2*C1*(1 - 2*C1)*e + 2*C1*(1 - C1)*\-3 - e + 6*C1/ + 2*C1*(-1 + C1)*e + 2*C1*(-1 + 2*C1)*e /*e - 12*C1 *(-1 + 2*C1)*e + 12*C1 *(1 - C1)*e + 2*C1*(1 - C1)*\- (1 - 2*C1) - 2*C1 + 2*C1 - C1*\-3 - e + 6*C1/ + 3*(1 - C1)*(-1 + 4*C1) + 3*(1 - 2*C1)*(-1 + 2*C1) + 8*C1*e /*e / / 6\
y(x) = C1 + C1*x*(1 - C1) + ----------------------------------- + --------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x /
2 6 24 120
$$y{\left(x \right)} = C_{1} + C_{1} x \left(1 - C_{1}\right) + \frac{C_{1} x^{2} \left(- C_{1} e^{3} + \left(1 - 2 C_{1}\right) \left(1 - C_{1}\right)\right)}{2} + \frac{C_{1} x^{3} \left(- C_{1} \left(1 - 2 C_{1}\right) e^{3} - 2 C_{1} \left(1 - C_{1}\right) e^{3} + \left(1 - C_{1}\right) \left(2 C_{1}^{2} - 2 C_{1} e^{3} - 2 C_{1} + \left(1 - 2 C_{1}\right)^{2}\right)\right)}{6} + \frac{C_{1} x^{4} \left(4 C_{1}^{2} e^{6} + 6 C_{1} \left(1 - C_{1}\right) \left(2 C_{1} - 1\right) e^{3} - C_{1} \left(2 C_{1}^{2} - 2 C_{1} e^{3} - 2 C_{1} + \left(1 - 2 C_{1}\right)^{2}\right) e^{3} + \left(1 - C_{1}\right) \left(2 C_{1}^{2} e^{3} - 2 C_{1} \left(1 - 2 C_{1}\right) e^{3} + 2 C_{1} \left(1 - C_{1}\right) \left(6 C_{1} - e^{3} - 3\right) + 2 C_{1} \left(C_{1} - 1\right) e^{3} + 2 C_{1} \left(2 C_{1} - 1\right) e^{3} + \left(1 - 2 C_{1}\right) \left(2 C_{1}^{2} - 2 C_{1} e^{3} - 2 C_{1} + \left(1 - 2 C_{1}\right)^{2}\right)\right)\right)}{24} + \frac{C_{1} x^{5} \left(12 C_{1}^{2} \left(1 - C_{1}\right) e^{6} - 12 C_{1}^{2} \left(2 C_{1} - 1\right) e^{6} + 2 C_{1} \left(1 - C_{1}\right) \left(- 2 C_{1}^{2} - C_{1} \left(6 C_{1} - e^{3} - 3\right) + 2 C_{1} + 8 C_{1} e^{3} - \left(1 - 2 C_{1}\right)^{2} + 3 \left(1 - 2 C_{1}\right) \left(2 C_{1} - 1\right) + 3 \left(1 - C_{1}\right) \left(4 C_{1} - 1\right)\right) e^{3} - C_{1} \left(2 C_{1}^{2} e^{3} - 2 C_{1} \left(1 - 2 C_{1}\right) e^{3} + 2 C_{1} \left(1 - C_{1}\right) \left(6 C_{1} - e^{3} - 3\right) + 2 C_{1} \left(C_{1} - 1\right) e^{3} + 2 C_{1} \left(2 C_{1} - 1\right) e^{3} + \left(1 - 2 C_{1}\right) \left(2 C_{1}^{2} - 2 C_{1} e^{3} - 2 C_{1} + \left(1 - 2 C_{1}\right)^{2}\right)\right) e^{3} + \left(1 - C_{1}\right) \left(- 2 C_{1}^{2} \left(6 C_{1} - e^{3} - 3\right) e^{3} + 12 C_{1}^{2} e^{6} + 6 C_{1} \left(1 - 2 C_{1}\right) \left(2 C_{1} - 1\right) e^{3} + 6 C_{1} \left(1 - C_{1}\right) \left(4 C_{1} - 1\right) e^{3} + 2 C_{1} \left(1 - C_{1}\right) \left(- 8 C_{1}^{2} + 8 C_{1} + 8 C_{1} e^{3} - \left(1 - 2 C_{1}\right)^{2} + 2 \left(1 - 2 C_{1}\right) \left(6 C_{1} - e^{3} - 3\right) + 3 \left(2 C_{1} - 1\right) e^{3}\right) - 2 C_{1} \left(2 C_{1}^{2} - 2 C_{1} e^{3} - 2 C_{1} + \left(1 - 2 C_{1}\right)^{2}\right) e^{3} + \left(1 - 2 C_{1}\right) \left(2 C_{1}^{2} e^{3} - 2 C_{1} \left(1 - 2 C_{1}\right) e^{3} + 2 C_{1} \left(1 - C_{1}\right) \left(6 C_{1} - e^{3} - 3\right) + 2 C_{1} \left(C_{1} - 1\right) e^{3} + 2 C_{1} \left(2 C_{1} - 1\right) e^{3} + \left(1 - 2 C_{1}\right) \left(2 C_{1}^{2} - 2 C_{1} e^{3} - 2 C_{1} + \left(1 - 2 C_{1}\right)^{2}\right)\right)\right)\right)}{120} + 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, 672148376.8061678)
(-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, 3.1237768967464496e-33)
(7.777777777777779, 8.388243571812249e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)