59.1.324 problem 331

Internal problem ID [9496]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 331
Date solved : Sunday, March 30, 2025 at 02:36:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

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

\[ y = c_1 \left (x^{3}-12 x^{2}+60 x -120\right )+c_2 \,{\mathrm e}^{-x} \left (x^{3}+12 x^{2}+60 x +120\right ) \]

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 98

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

\[ y(x)\to \frac {2 e^{-x/2} \sqrt {x} \left (\left (c_1 x^3+12 i c_2 x^2+60 c_1 x+120 i c_2\right ) \cosh \left (\frac {x}{2}\right )-\left (12 c_1 \left (x^2+10\right )+i c_2 x \left (x^2+60\right )\right ) \sinh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) + (x - 6)*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None