23.3.466 problem 472

Internal problem ID [6180]
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 : 472
Date solved : Tuesday, September 30, 2025 at 02:24:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} -12 y-2 \left (1+2 x \right ) y^{\prime }+\left (1+2 x \right )^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=-12*y(x)-2*(2*x+1)*diff(y(x),x)+(2*x+1)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {16 \left (x +\frac {1}{2}\right )^{4} c_2 +16 c_1}{8+16 x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 26

ode=-12*y[x] - 2*(1 + 2*x)*D[y[x],x] + (1 + 2*x)^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x + 1)**2*Derivative(y(x), (x, 2)) - (4*x + 2)*Derivative(y(x), x) - 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False