78.8.24 problem 24

Internal problem ID [18222]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 11:40:41 AM
CAS classification : [NONE]

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

✗ Solution by Maple

dsolve((x*exp(y(x))+y(x)-x^2)*diff(y(x),x$2)=2*x*y(x)-exp(y(x))-x,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(x*Exp[y[x]]+y[x]-x^2)*D[y[x],{x,2}]==2*x*y[x]-Exp[y[x]]-x,y[x],x,IncludeSingularSolutions -> True]
 

Not solved