23.3.442 problem 447

Internal problem ID [6156]
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 : 447
Date solved : Tuesday, September 30, 2025 at 02:23:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\[ y = \sqrt {1+x}\, c_1 +\left (1+x \right ) \ln \left (1+x \right )+\left (c_2 -2\right ) x +c_2 -3 \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to (x+1) \log (x+1)+c_1 \sqrt {x+1}+(-2+c_2) x-3+c_2 \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (2*x**2*Derivative(y(x), (x, 2)) + 4*x*Der