59.1.77 problem 79

Internal problem ID [9249]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 79
Date solved : Sunday, March 30, 2025 at 02:30:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=(4*x+2)*diff(diff(y(x),x),x)-4*diff(y(x),x)-(6+4*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.345 (sec). Leaf size: 69

ode=(2+4*x)*D[y[x],{x,2}]-4*D[y[x],x]-(6+4*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {2 x+1} \exp \left (\int _1^x\left (\frac {1}{-2 K[1]-1}-1\right )dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\left (\frac {1}{-2 K[1]-1}-1\right )dK[1]\right )dK[2]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((4*x + 2)*Derivative(y(x), (x, 2)) - (4*x + 6)*y(x) - 4*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False