56.5.19 problem 19

Internal problem ID [8980]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:26:09 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }&=\frac {y}{2 y \ln \left (y\right )+y-x} \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 19

dsolve(diff(y(x),x)=y(x)/(2*y(x)*ln(y(x))+y(x)-x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 19

DSolve[D[y[x],x]==y[x]/(2*y[x]*Log[y[x]]+y[x]-x),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=y(x) \log (y(x))+\frac {c_1}{y(x)},y(x)\right ] \]