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Ecuación diferencial dy/dx=xy^2-cos(x)sin(x)/y(1-x^2)

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Para el problema de Cauchy:

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

Gráfico:

interior superior

Solución

Ha introducido [src]
                     /     2\              
d             2      \1 - x /*cos(x)*sin(x)
--(y(x)) = x*y (x) - ----------------------
dx                            y(x)         
$$\frac{d}{d x} y{\left(x \right)} = x y^{2}{\left(x \right)} - \frac{\left(1 - x^{2}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{y{\left(x \right)}}$$
y' = x*y^2 - (1 - x^2)*sin(x)*cos(x)/y
Respuesta [src]
                             4 /10     / 1        \ /  2   1 \\        
             2 /  2   1 \   x *|-- + 3*|--- + 2*C1|*|C1  - --||        
            x *|C1  - --|      |C1     |  2       | \      C1/|        
               \      C1/      \       \C1        /           /    / 6\
y(x) = C1 + ------------- + ----------------------------------- + O\x /
                  2                          24                        
$$y{\left(x \right)} = \frac{x^{2} \left(C_{1}^{2} - \frac{1}{C_{1}}\right)}{2} + \frac{x^{4} \left(3 \left(2 C_{1} + \frac{1}{C_{1}^{2}}\right) \left(C_{1}^{2} - \frac{1}{C_{1}}\right) + \frac{10}{C_{1}}\right)}{24} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st power series
lie group