59.1.311 problem 316

Internal problem ID [9483]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 316
Date solved : Sunday, March 30, 2025 at 02:35:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 31

ode:=(x^2-2*x+10)*diff(diff(y(x),x),x)+x*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3 c_2 \left (x -1+3 i\right )^{\frac {1}{2}-\frac {i}{6}} \left (x -\frac {4}{3}\right ) \left (x -1-3 i\right )^{\frac {1}{2}+\frac {i}{6}}+c_1 \left (x^{2}-\frac {4}{3} x +5\right ) \]

✓ Mathematica. Time used: 0.754 (sec). Leaf size: 125

ode=(x^2-2*x+10)*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} (3 x-4) \exp \left (\int _1^x\frac {3 K[1]-4}{2 (K[1]-2) K[1]+20}dK[1]-\frac {1}{2} \int _1^x\frac {K[2]}{(K[2]-2) K[2]+10}dK[2]\right ) \left (c_2 \int _1^x\frac {9 \exp \left (-2 \int _1^{K[3]}\frac {3 K[1]-4}{2 \left (K[1]^2-2 K[1]+10\right )}dK[1]\right )}{(4-3 K[3])^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (x**2 - 2*x + 10)*Derivative(y(x), (x, 2)) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False