78.8.24 problem 24

Internal problem ID [18143]
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 : Thursday, March 13, 2025 at 11:43:05 AM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + x + (-x**2 + x*exp(y(x)) + y(x))*Derivative(y(x), (x, 2)) + exp(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -2*x*y(x) + x + (-x**2 + x*exp(y(x)) + y(x))*Derivative(y(x), (x, 2)) + exp(y(x))