23.3.416 problem 421

Internal problem ID [6130]
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 : 421
Date solved : Tuesday, September 30, 2025 at 02:22:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-4 \left (1+x \right ) y^{\prime }+\left (1+x \right )^{2} y^{\prime \prime }&=x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=6*y(x)-4*(1+x)*diff(y(x),x)+(1+x)^2*diff(diff(y(x),x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (1+x \right )^{3} c_2 +\left (1+x \right )^{2} c_1 -\frac {x^{2}}{3}-\frac {x}{6} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 31

ode=6*y[x] - 4*(1 + x)*D[y[x],x] + (1 + x)^2*D[y[x],{x,2}] == x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} (3 x+2)+c_2 (x+1)^3+c_1 (x+1)^2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (x + 1)**2*Derivative(y(x), (x, 2)) - (4*x + 4)*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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