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Ecuación diferencial (cos(x)sin(x)-xy^2)dx+y(1-x^2)dy=0

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Para el problema de Cauchy:

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

Gráfico:

interior superior

Solución

Ha introducido [src]
d                                  2       2 d                
--(y(x))*y(x) + cos(x)*sin(x) - x*y (x) - x *--(y(x))*y(x) = 0
dx                                           dx               
$$- x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - x y^{2}{\left(x \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} = 0$$
-x^2*y*y' - x*y^2 + y*y' + sin(x)*cos(x) = 0
Respuesta [src]
                   _______________ 
          ___     / C1 - cos(2*x)  
       -\/ 2 *   /  -------------  
                /            2     
              \/       -1 + x      
y(x) = ----------------------------
                    2              
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{\frac{C_{1} - \cos{\left(2 x \right)}}{x^{2} - 1}}}{2}$$
                  _______________
         ___     / C1 - cos(2*x) 
       \/ 2 *   /  ------------- 
               /            2    
             \/       -1 + x     
y(x) = --------------------------
                   2             
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{\frac{C_{1} - \cos{\left(2 x \right)}}{x^{2} - 1}}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
Bernoulli
1st power series
lie group
1st exact Integral
Bernoulli Integral
Respuesta numérica [src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.9735285479359161)
(-5.555555555555555, 1.3673306588017893)
(-3.333333333333333, 2.3413406649946187)
(-1.1111111111111107, 15.47795464139391)
(1.1111111111111107, 4663581.254556012)
(3.333333333333334, 1.686592637976697e-51)
(5.555555555555557, 8.735934836677909e+189)
(7.777777777777779, 2.5718481162063698e+151)
(10.0, -3.127441380144104e-210)
(10.0, -3.127441380144104e-210)