72.7.9 problem 9

Internal problem ID [14671]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 9
Date solved : Thursday, March 13, 2025 at 04:13:28 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 11

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

\[ y = t +\frac {2}{t} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 12

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

\[ y(t)\to t+\frac {2}{t} \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = t + \frac {2}{t} \]