Internal problem ID [8385]
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]
\[ \boxed {y^{\prime }+\frac {1}{-x -f_{1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}}=0} \]
✓ Solution by Maple
Time used: 0.032 (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)
\[ \frac {\ln \left (x \right )^{2}}{2}-y \left (x \right ) \ln \left (x \right )-\left (\int _{}^{y \left (x \right )-\ln \left (x \right )}\frac {f_{1} \left (\textit {\_a} \right ) \textit {\_a} +{\mathrm e}^{-\textit {\_a}}}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 57
DSolve[y'[x] == -(-x - E^y[x]*F1[-Log[x] + y[x]]*y[x])^(-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\int _1^{y(x)-\log (x)}\frac {\text {F1}(K[1]) K[1]+e^{-K[1]}}{\text {F1}(K[1])}dK[1]-y(x) \log (x)+\frac {\log ^2(x)}{2}=-c_1,y(x)\right ] \]