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Ecuaciones diferenciales/ ((sin(y))^0.5+3x^2*cos(y))dx+((x*cos(y))/(2(sin(y))^0.5)-x^3*sin(y))dy=0

Ecuación diferencial ((sin(y))^0.5+3x^2*cos(y))dx+((x*cos(y))/(2(sin(y))^0.5)-x^3*sin(y))dy=0

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Para el problema de Cauchy:

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

Gráfico:

interior superior
⌨

Solución

Ha introducido [src] 
                                                           d                     
                                                         x*--(y(x))*cos(y(x))    
  ___________      2              3 d                      dx                    
\/ sin(y(x))  + 3*x *cos(y(x)) - x *--(y(x))*sin(y(x)) + -------------------- = 0
                                    dx                         ___________       
                                                           2*\/ sin(y(x))
$$- x^{3} \sin{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + 3 x^{2} \cos{\left(y{\left(x \right)} \right)} + \frac{x \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)}}{2 \sqrt{\sin{\left(y{\left(x \right)} \right)}}} + \sqrt{\sin{\left(y{\left(x \right)} \right)}} = 0$$ 
-x^3*sin(y)*y' + 3*x^2*cos(y) + x*cos(y)*y'/(2*sqrt(sin(y))) + sqrt(sin(y)) = 0
Gráfico para el problema de Cauchy
Respuesta numérica [src] 
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.033446911577209366)
(-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, 6.397106897951207e+170)
(7.777777777777779, 8.388243571811068e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)
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