66.3.11 problem 15

Internal problem ID [15962]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.4 page 61
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:33:13 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 14

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

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

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants