59.1.173 problem 175

Internal problem ID [9345]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 175
Date solved : Sunday, March 30, 2025 at 02:32:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 50

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

\[ y = \frac {-c_2 \left (x^{5}-x^{4}+2 x^{3}-6 x^{2}+24 x -120\right ) {\mathrm e}^{-x}+x^{6} \left (c_2 \,\operatorname {Ei}_{1}\left (x \right )+c_1 \right )}{x^{3}} \]

✓ Mathematica. Time used: 0.367 (sec). Leaf size: 40

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

\[ y(x)\to e^{7/2} x^3 \left (c_2 \int _1^x\frac {e^{-K[1]-7}}{K[1]^7}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(x + 1)*Derivative(y(x), x) - (3*x + 9)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False