23.3.419 problem 424

Internal problem ID [6133]
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 : 424
Date solved : Tuesday, September 30, 2025 at 02:22:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (3+2 x \right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=-(2*x+3)*y(x)+(x^2+x+1)*diff(y(x),x)+(x^2+3*x+4)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-x}+c_2 \left (x^{2}+x +3\right ) \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 23

ode=-((3 + 2*x)*y[x]) + (1 + x + x^2)*D[y[x],x] + (4 + 3*x + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 \left (x^2+x+3\right )+c_1 e^{-x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x - 3)*y(x) + (x**2 + x + 1)*Derivative(y(x), x) + (x**2 + 3*x + 4)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False