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Ecuaciones diferenciales/ y'=-y*tgx+(1/sin^3(x))*(1/y)

Ecuación diferencial y'=-y*tgx+(1/sin^3(x))*(1/y)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Para el problema de Cauchy:

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

Gráfico:

interior superior
⌨

Solución

Ha introducido [src] 
d               1                    
--(y(x)) = ------------ - tan(x)*y(x)
dx            3                      
           sin (x)*y(x)
$$\frac{d}{d x} y{\left(x \right)} = - y{\left(x \right)} \tan{\left(x \right)} + \frac{1}{y{\left(x \right)} \sin^{3}{\left(x \right)}}$$ 
y' = -y*tan(x) + 1/(y*sin(x)^3)
Respuesta [src] 
                    _________________________________________________________________________________________________________________________________________________________________ 
                   / /         2                        3           3                                                       3                                               \         
          ___     /  \4 - 6*cos (x) + C1*cos(x) - C1*cos (x) - 3*cos (x)*log(-1 + cos(x)) - 3*cos(x)*log(1 + cos(x)) + 3*cos (x)*log(1 + cos(x)) + 3*cos(x)*log(-1 + cos(x))/*cos(x)  
       -\/ 2 *   /   ---------------------------------------------------------------------------------------------------------------------------------------------------------------  
                /                                                                                   2                                                                                 
              \/                                                                                 sin (x)                                                                              
y(x) = -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                              2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{\frac{\left(- C_{1} \cos^{3}{\left(x \right)} + C_{1} \cos{\left(x \right)} - 3 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos^{3}{\left(x \right)} + 3 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos{\left(x \right)} + 3 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos^{3}{\left(x \right)} - 3 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)} - 6 \cos^{2}{\left(x \right)} + 4\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}}}}{2}$$
Trazar el gráfico con C=-1
Trazar el gráfico con C=0
Trazar el gráfico con C=1 
                   _________________________________________________________________________________________________________________________________________________________________
                  / /         2                        3           3                                                       3                                               \        
         ___     /  \4 - 6*cos (x) + C1*cos(x) - C1*cos (x) - 3*cos (x)*log(-1 + cos(x)) - 3*cos(x)*log(1 + cos(x)) + 3*cos (x)*log(1 + cos(x)) + 3*cos(x)*log(-1 + cos(x))/*cos(x) 
       \/ 2 *   /   --------------------------------------------------------------------------------------------------------------------------------------------------------------- 
               /                                                                                   2                                                                                
             \/                                                                                 sin (x)                                                                             
y(x) = -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                             2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{\frac{\left(- C_{1} \cos^{3}{\left(x \right)} + C_{1} \cos{\left(x \right)} - 3 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos^{3}{\left(x \right)} + 3 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos{\left(x \right)} + 3 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos^{3}{\left(x \right)} - 3 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)} - 6 \cos^{2}{\left(x \right)} + 4\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}}}}{2}$$
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
Bernoulli
lie group
Bernoulli Integral
Respuesta numérica [src] 
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 4125677.11593307)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 8.973398002470273e-67)
(7.777777777777779, 8.388243571810392e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)
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