90.4.24 problem 25

Internal problem ID [25119]
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 : 25
Date solved : Thursday, October 02, 2025 at 11:50:42 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

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

\[ y = \frac {t +4 a -2}{t^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

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

\begin{align*} y(t)&\to \frac {4 a+t-2}{t^2} \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \frac {4 a + t - 2}{t^{2}} \]