23.3.399 problem 403

Internal problem ID [6113]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 403
Date solved : Tuesday, September 30, 2025 at 02:21:44 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} y+\left (2+3 x \right ) y^{\prime }+x \left (1+x \right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=y(x)+(2+3*x)*diff(y(x),x)+x*(1+x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \ln \left (1+x \right )+c_2}{x} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 28

ode=y[x] + (2 + 3*x)*D[y[x],x] + x*(1 + x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 \log (2 (x+1))+2 c_1}{\sqrt {2} x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x + 1)*Derivative(y(x), (x, 2)) + (3*x + 2)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False