59.1.407 problem 419

Internal problem ID [9579]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 419
Date solved : Wednesday, March 05, 2025 at 07:51:12 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 31

ode:=(x^2-6*x+10)*diff(diff(y(x),x),x)-4*(x-3)*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} x^{3}+c_{2} x^{2}+6 \left (-5 c_{1} -c_{2} \right ) x +60 c_{1} +\frac {26 c_{2}}{3} \]

✓ Mathematica. Time used: 0.297 (sec). Leaf size: 84

ode=(x^2-6*x+10)*D[y[x],{x,2}]-4*(x-3)*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \left (x^2-6 x+10\right ) \exp \left (\int _1^x\frac {K[1]-(3-3 i)}{(K[1]-6) K[1]+10}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\frac {K[1]-(3-3 i)}{(K[1]-6) K[1]+10}dK[1]\right )dK[2]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((12 - 4*x)*Derivative(y(x), x) + (x**2 - 6*x + 10)*Derivative(y(x), (x, 2)) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False