59.1.263 problem 266

Internal problem ID [9435]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 266
Date solved : Wednesday, March 05, 2025 at 07:49:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 38

ode:=x^2*diff(diff(y(x),x),x)+(x^2+x)*diff(y(x),x)+(x-9)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{2} {\mathrm e}^{-x} \left (x^{3}+9 x^{2}+36 x +60\right )+c_{1} \left (x^{2}-8 x +20\right )}{x^{3}} \]

✓ Mathematica. Time used: 0.626 (sec). Leaf size: 96

ode=x^2*D[y[x],{x,2}]+(x+x^2)*D[y[x],x]+(x-9)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (x^2-8 x+20\right ) \exp \left (\int _1^x\frac {K[1]-5}{2 K[1]}dK[1]-\frac {x}{2}\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[2]}\frac {K[1]-5}{2 K[1]}dK[1]\right )}{\left (K[2]^2-8 K[2]+20\right )^2}dK[2]+c_1\right )}{\sqrt {x}} \]

✗ Sympy

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

False