90.4.14 problem 15

Internal problem ID [25109]
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 : 15
Date solved : Thursday, October 02, 2025 at 11:50:26 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=-3 \\ \end{align*}

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

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

\[ y = -\frac {1}{2}-t -\frac {3}{2} t^{2} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {1}{2} \left (-3 t^2-2 t-1\right ) \end{align*}

✓ Sympy. Time used: 0.152 (sec). Leaf size: 15

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

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