Internal problem ID [6559]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{2 y \ln \relax (y)+y-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 19
dsolve(diff(y(x),x)=y(x)/(2*y(x)*ln(y(x))+y(x)-x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} -{\mathrm e}^{\textit {\_Z}} x +c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.302 (sec). Leaf size: 19
DSolve[y'[x]==y[x]/(2*y[x]*Log[y[x]]+y[x]-x),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=y(x) \log (y(x))+\frac {c_1}{y(x)},y(x)\right ] \]