23.3.116 problem 118

Internal problem ID [5830]
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 : 118
Date solved : Tuesday, September 30, 2025 at 02:03:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

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

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

✗ Sympy

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

False