23.3.359 problem 363

Internal problem ID [6073]
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 : 363
Date solved : Tuesday, September 30, 2025 at 02:21:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

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

\[ y = c_1 x +\arctan \left (x \right ) x c_2 +c_2 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 48

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

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

✗ Sympy

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

False