60.2.231 problem 807

Internal problem ID [10818]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 807
Date solved : Tuesday, January 28, 2025 at 05:17:24 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \end{align*}

✓ Solution by Maple

Time used: 0.066 (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)
 

\[ \frac {\ln \left (x \right )^{2}}{2}-y \ln \left (x \right )-\int _{}^{y-\ln \left (x \right )}\frac {f_{1} \left (\textit {\_a} \right ) \textit {\_a} +{\mathrm e}^{-\textit {\_a}}}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.234 (sec). Leaf size: 57

DSolve[D[y[x],x] == -(-x - E^y[x]*F1[-Log[x] + y[x]]*y[x])^(-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\int _1^{y(x)-\log (x)}\frac {\text {F1}(K[1]) K[1]+e^{-K[1]}}{\text {F1}(K[1])}dK[1]-y(x) \log (x)+\frac {\log ^2(x)}{2}=-c_1,y(x)\right ] \]