54.3.268 problem 1284

Internal problem ID [12563]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1284
Date solved : Wednesday, October 01, 2025 at 02:06:44 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1&=0 \end{align*}

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

ode:=(2*x+1)^2*diff(diff(y(x),x),x)-2*(2*x+1)*diff(y(x),x)-12*y(x)-3*x-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 41

ode=-1 - 3*x - 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 \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*Derivative(y(x), (x, 2)) - 3*x - 12*y(x) + Derivative(y(x), (x, 2)) - 1)/(2*(2*x + 1)) cannot be solved by the factorable group method