90.25.11 problem 11

Internal problem ID [25392]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 379
Problem number : 11
Date solved : Friday, October 03, 2025 at 12:00:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+y&=t \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=t^2*diff(diff(y(t),t),t)-t*diff(y(t),t)+y(t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = t \left (c_2 +c_1 \ln \left (t \right )+\frac {\ln \left (t \right )^{2}}{2}\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 25

ode=t^2*D[y[t],{t,2}]-t*D[y[t],t]+y[t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{2} t \left (\log ^2(t)+2 c_2 \log (t)+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {t \left (C_{1} + C_{2} \log {\left (t \right )} + \log {\left (t \right )}^{2}\right )}{2} \]