77.1.118 problem 145 (page 213)

Internal problem ID [17937]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 145 (page 213)
Date solved : Monday, March 31, 2025 at 04:51:56 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: 0.003 (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: 0.248 (sec). Leaf size: 27

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]
 

\[ y(x)\to \frac {1}{2} c_2 \left (4 x^2+1\right )+c_1 e^{-2 x} \]

✗ 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