23.3.467 problem 473

Internal problem ID [6181]
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 : 473
Date solved : Tuesday, September 30, 2025 at 02:24:14 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} -12 y-2 \left (1+2 x \right ) y^{\prime }+\left (1+2 x \right )^{2} y^{\prime \prime }&=1+3 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

ode:=-12*y(x)-2*(2*x+1)*diff(y(x),x)+(2*x+1)^2*diff(diff(y(x),x),x) = 3*x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{1+2 x}+\left (1+2 x \right )^{3} c_2 +\frac {-72 x^{2}-56 x -7}{192+384 x} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 41

ode=-12*y[x] - 2*(1 + 2*x)*D[y[x],x] + (1 + 2*x)^2*D[y[x],{x,2}] == 1 + 3*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-72 x^2-56 x+192 c_1 (2 x+1)^4-7+192 c_2}{192 (2 x+1)} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + (2*x + 1)**2*Derivative(y(x), (x, 2)) - (4*x + 2)*Derivative(y(x), x) - 12*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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