Internal problem ID [8387]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 807.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {1}{-x -f_{1}\left (y-\ln \relax (x )\right ) y \,{\mathrm e}^{y}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.095 (sec). Leaf size: 43
dsolve(diff(y(x),x) = -1/(-x-_F1(y(x)-ln(x))*y(x)*exp(y(x))),y(x), singsol=all)
\[ \frac {\ln \relax (x )^{2}}{2}-y \relax (x ) \ln \relax (x )-\left (\int _{}^{y \relax (x )-\ln \relax (x )}\frac {f_{1}\left (\textit {\_a} \right ) \textit {\_a} +{\mathrm e}^{-\textit {\_a}}}{f_{1}\left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.288 (sec). Leaf size: 57
DSolve[y'[x] == -(-x - E^y[x]*F1[-Log[x] + y[x]]*y[x])^(-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\int _1^{y(x)-\log (x)}\frac {\text {F1}(K[1]) K[1]+e^{-K[1]}}{\text {F1}(K[1])}dK[1]-y(x) \log (x)+\frac {\log ^2(x)}{2}=-c_1,y(x)\right ] \]