90.25.9 problem 9

Internal problem ID [25390]
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 : 9
Date solved : Friday, October 03, 2025 at 12:00:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=t^{4} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=t^2*diff(diff(y(t),t),t)-2*t*diff(y(t),t)+2*y(t) = t^4; 
dsolve(ode,y(t), singsol=all);
 

\[ y = t c_2 +t^{2} c_1 +\frac {1}{6} t^{4} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

ode=t^2*D[y[t],{t,2}]-2*t*D[y[t],t]+2*y[t]==t^4; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{6} t \left (t^3+6 c_2 t+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.214 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = t \left (C_{1} + C_{2} t + \frac {t^{3}}{6}\right ) \]