69.20.1 problem 636

Internal problem ID [18422]
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 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 636
Date solved : Thursday, October 02, 2025 at 03:11:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=(2*x+1)*diff(diff(y(x),x),x)+(4*x-2)*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 4 c_1 \,x^{2}+c_2 \,{\mathrm e}^{-2 x}+c_1 \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 92

ode=(2*x+1)*D[y[x],{x,2}]+(4*x-2)*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\left (-1-\frac {2}{2 K[1]+1}\right )dK[1]-\frac {1}{2} \int _1^x\left (2-\frac {4}{2 K[2]+1}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}-\frac {2 K[1]+3}{2 K[1]+1}dK[1]\right )dK[3]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x + 1)*Derivative(y(x), (x, 2)) + (4*x - 2)*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False