90.3.10 problem 10

Internal problem ID [25074]
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 41
Problem number : 10
Date solved : Thursday, October 02, 2025 at 11:49:15 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.211 (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(2): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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