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Ecuaciones diferenciales/ y'=1+0.2*sin(x)-y^2

Ecuación diferencial y'=1+0.2*sin(x)-y^2

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Para el problema de Cauchy:

y() =
y'() =
y''() =
y'''() =
y''''() =

Gráfico:

interior superior
⌨

Solución

Ha introducido [src] 
d               2      sin(x)
--(y(x)) = 1 - y (x) + ------
dx                       5
$$\frac{d}{d x} y{\left(x \right)} = - y^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{5} + 1$$ 
y' = -y^2 + sin(x)/5 + 1
Respuesta [src] 
                                                                                                /         2                                                        \      /                                                                                                                    /         2\         /      2\\        
                           2 /1        /      2\\    3 /  2*C1     /      2\ /         2\\    4 |     8*C1    /      2\ /  2        /         2\         /      2\\|    5 |  6    2*C1   /      2\ /16*C1        /  2        /         2\         /      2\\     /      2\ /        2\\   4*C1*\-1 + 3*C1 /   28*C1*\1 - C1 /|        
                          x *|- - 2*C1*\1 - C1 /|   x *|- ---- + 2*\1 - C1 /*\-1 + 3*C1 /|   x *|-1 + ----- + \1 - C1 /*|- - - 4*C1*\-1 + 3*C1 / + 12*C1*\1 - C1 /||   x *|- -- + ---- + \1 - C1 /*|----- - 2*C1*|- - - 4*C1*\-1 + 3*C1 / + 12*C1*\1 - C1 /| + 8*\1 - C1 /*\2 - 9*C1 /| - ----------------- + ---------------|        
              /      2\      \5                 /      \   5                             /      \       5               \  5                                      //      \  25    5               \  5          \  5                                      /                          /           5                  5       /    / 6\
y(x) = C1 + x*\1 - C1 / + ----------------------- + -------------------------------------- + ----------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x /
                                     2                                6                                                         24                                                                                                               120
$$y{\left(x \right)} = x \left(1 - C_{1}^{2}\right) + \frac{x^{2} \left(- 2 C_{1} \left(1 - C_{1}^{2}\right) + \frac{1}{5}\right)}{2} + \frac{x^{3} \left(- \frac{2 C_{1}}{5} + 2 \left(1 - C_{1}^{2}\right) \left(3 C_{1}^{2} - 1\right)\right)}{6} + \frac{x^{4} \left(\frac{8 C_{1}^{2}}{5} + \left(1 - C_{1}^{2}\right) \left(12 C_{1} \left(1 - C_{1}^{2}\right) - 4 C_{1} \left(3 C_{1}^{2} - 1\right) - \frac{2}{5}\right) - 1\right)}{24} + \frac{x^{5} \left(\frac{28 C_{1} \left(1 - C_{1}^{2}\right)}{5} - \frac{4 C_{1} \left(3 C_{1}^{2} - 1\right)}{5} + \frac{2 C_{1}}{5} + \left(1 - C_{1}^{2}\right) \left(- 2 C_{1} \left(12 C_{1} \left(1 - C_{1}^{2}\right) - 4 C_{1} \left(3 C_{1}^{2} - 1\right) - \frac{2}{5}\right) + \frac{16 C_{1}}{5} + 8 \left(1 - C_{1}^{2}\right) \left(2 - 9 C_{1}^{2}\right)\right) - \frac{6}{25}\right)}{120} + C_{1} + O\left(x^{6}\right)$$
Trazar el gráfico con C=-1
Trazar el gráfico con C=0
Trazar el gráfico con C=1
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica [src] 
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.9104719031400728)
(-5.555555555555555, 1.0225800325772507)
(-3.333333333333333, 1.0520020064236617)
(-1.1111111111111107, 0.90740362544258)
(1.1111111111111107, 1.0531722739983598)
(3.333333333333334, 1.0224925619370206)
(5.555555555555557, 0.9132664762574088)
(7.777777777777779, 1.0751705825210183)
(10.0, 0.9893029343294817)
(10.0, 0.9893029343294817)
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