Internal problem ID [3944]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 698.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {x \left (x +y+2 y^{3}\right ) y^{\prime }-\left (-y+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(x*(x+y(x)+2*y(x)^3)*diff(y(x),x) = (x-y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+{\mathrm e}^{\textit {\_Z}} c_{1} -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]
✓ Solution by Mathematica
Time used: 0.322 (sec). Leaf size: 23
DSolve[x(x+y[x]+2 y[x]^3)y'[x]==(x-y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))+\log (x)=c_1,y(x)\right ] \]