59.1.75 problem 77

Internal problem ID [9247]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 77
Date solved : Wednesday, March 05, 2025 at 07:46:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

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

\[ y = \left (\left (x^{2}+3 x +9\right ) \left (x^{2}+9 x +27\right ) \left (6+x \right ) c_{2} x +c_{1} \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.329 (sec). Leaf size: 52

ode=(3+x)*D[y[x],{x,2}]+(1+2*x)*D[y[x],x]-(2-x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (c_2 (x+3)^6+6 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (2-\frac {5}{K[1]+3}\right )dK[1]\right )}{6 (x+3)^{5/2}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 2)*y(x) + (x + 3)*Derivative(y(x), (x, 2)) + (2*x + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False