90.4.22 problem 23

Internal problem ID [25117]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 23
Date solved : Thursday, October 02, 2025 at 11:50:39 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (-1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 14

ode:=t*diff(y(t),t)+3*y(t) = t^2; 
ic:=[y(-1) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {t^{5}-9}{5 t^{3}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to \frac {t^5-9}{5 t^3} \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = \frac {\frac {t^{5}}{5} - \frac {9}{5}}{t^{3}} \]