11.3.2 problem 1.1-4 (b)

Internal problem ID [3432]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-4, page 7
Problem number : 1.1-4 (b)
Date solved : Tuesday, September 30, 2025 at 06:38:08 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(y(t),t) = -t/y(t); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \sqrt {-t^{2}+c_1} \\ y &= -\sqrt {-t^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 39

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

\begin{align*} y(t)&\to -\sqrt {-t^2+2 c_1}\\ y(t)&\to \sqrt {-t^2+2 c_1} \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 22

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

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