59.1.305 problem 309

Internal problem ID [9477]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 309
Date solved : Wednesday, March 05, 2025 at 07:49:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 44

ode:=diff(diff(y(x),x),x)-2*x*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 c_{1} \left (2 x^{3}-5 x \right ) {\mathrm e}^{x^{2}}-4 \left (\operatorname {erfi}\left (x \right ) \sqrt {\pi }\, c_{1} -c_{2} \right ) \left (x^{4}-3 x^{2}+\frac {3}{4}\right ) \]

✓ Mathematica. Time used: 1.176 (sec). Leaf size: 58

ode=D[y[x],{x,2}]-2*x*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (4 x^4-12 x^2+3\right ) \left (c_2 \int _1^x\frac {16 e^{K[1]^2}}{\left (4 K[1]^4-12 K[1]^2+3\right )^2}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) + 8*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False