36.7 problem Ex 7

Internal problem ID [11329]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60. Exact equation. Integrating factor. Page 139
Problem number: Ex 7.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-y^{\prime } x^{3}-2 y=0} \]

✗ Solution by Maple

dsolve(x^2*(1-x^3)*diff(y(x),x$2)-x^3*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[x^2*(1-x^3)*y''[x]-x^3*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved