68.6.31 problem 32

Internal problem ID [17341]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 32
Date solved : Thursday, October 02, 2025 at 02:06:04 PM
CAS classification : [_linear]

\begin{align*} 1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 11

ode:=1+1/t^2*y(t)-1/t*diff(y(t),t) = 0; 
ic:=[y(2) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 14

ode=(1+y[t]/t^2)-1/t*D[y[t],t]==0; 
ic={y[2]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 8

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

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