23.4.81 problem 81

Internal problem ID [6383]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 81
Date solved : Tuesday, September 30, 2025 at 02:54:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=b*exp(y(x))*x+a*diff(y(x),x)+x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=b*E^y[x]*x + a*D[y[x],x] + x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - x*(-b*exp(y(x)) - Derivative(y(x), (x, 2))