23.3.226 problem 228

Internal problem ID [5940]
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 : 228
Date solved : Tuesday, September 30, 2025 at 02:06:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = c_2 x +{\mathrm e}^{x} c_1 +x^{2}+1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to x^2+x-c_2 x+c_1 e^x+1 \end{align*}

✗ Sympy

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

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