90.25.10 problem 10

Internal problem ID [25391]
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 : 10
Date solved : Friday, October 03, 2025 at 12:00:52 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=t*diff(diff(y(t),t),t)-diff(y(t),t) = 3*t^2-1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = t^{3}+\frac {1}{2} c_1 \,t^{2}+t +c_2 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 21

ode=t*D[y[t],{t,2}]-D[y[t],t]==3*t^2-1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t^3+\frac {c_1 t^2}{2}+t+c_2 \end{align*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t**2 + t*Derivative(y(t), (t, 2)) - Derivative(y(t), t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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