90.7.11 problem 11

Internal problem ID [25165]
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 99
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:55:55 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 14

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

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