80.5.69 problem D 20

Internal problem ID [21290]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 5. Second order equations. Excercise 5.9 at page 119
Problem number : D 20
Date solved : Thursday, October 02, 2025 at 07:27:53 PM
CAS classification : [_Hermite]

\begin{align*} x^{\prime \prime }-x^{\prime } t +3 x&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 26

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

\[ x = -\frac {c_1 t \left (t^{2}-3\right )}{3}+c_2 \operatorname {hypergeom}\left (\left [-\frac {3}{2}\right ], \left [\frac {1}{2}\right ], \frac {t^{2}}{2}\right ) \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 97

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

\begin{align*} x(t)&\to \frac {1}{4} \left (\sqrt {2 \pi } c_2 \sqrt {t^2} \left (t^2-3\right ) \text {erfi}\left (\frac {\sqrt {t^2}}{\sqrt {2}}\right )+8 \sqrt {2} c_1 t^3-2 c_2 e^{\frac {t^2}{2}} t^2+4 c_2 e^{\frac {t^2}{2}}-24 \sqrt {2} c_1 t\right ) \end{align*}

✗ Sympy

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

False