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Ecuación diferencial dx*(-5*x^2*y^2+3*x)+dy*(-10*x^3*y/3+3*y^2)=0

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]
                                          3 d                
                                      10*x *--(y(x))*y(x)    
         2  2         2    d                dx               
3*x - 5*x *y (x) + 3*y (x)*--(y(x)) - ------------------- = 0
                           dx                  3             
$$- \frac{10 x^{3} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{3} - 5 x^{2} y^{2}{\left(x \right)} + 3 x + 3 y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-10*x^3*y*y'/3 - 5*x^2*y^2 + 3*x + 3*y^2*y' = 0
Respuesta [src]
               3      2       4         
            5*x      x       x      / 6\
y(x) = C1 + ---- - ----- - ----- + O\x /
             9         2       5        
                   2*C1    4*C1         
$$y{\left(x \right)} = - \frac{x^{4}}{4 C_{1}^{5}} - \frac{x^{2}}{2 C_{1}^{2}} + \frac{5 x^{3}}{9} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral