68.3.32 problem 27

Internal problem ID [17179]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 27
Date solved : Thursday, October 02, 2025 at 01:49:24 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \\ \end{align*}

✓ Maple. Time used: 0.083 (sec). Leaf size: 15

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

\[ y = \frac {\sqrt {-4 t^{2}+1}}{2} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 20

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

\begin{align*} y(t)&\to \frac {1}{2} \sqrt {1-4 t^2} \end{align*}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \sqrt {\frac {1}{4} - t^{2}} \]