75.19.6 problem 623

Internal problem ID [17051]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 623
Date solved : Monday, March 31, 2025 at 03:39:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=(2*x+1)^2*diff(diff(y(x),x),x)-2*(2*x+1)*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 23

ode=(2*x+1)^2*D[y[x],{x,2}]-2*(2*x+1)*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (2 x+1) (c_2 \log (2 x+1)+c_1) \]

✗ 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) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False