68.3.5 problem 4

Internal problem ID [17152]
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 : 4
Date solved : Thursday, October 02, 2025 at 01:45:12 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to 0\\ y(t)&\to \frac {t^4}{16} \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = \frac {t^{4}}{16} \]