57.4.1 problem 1(a)

Internal problem ID [14325]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 1(a)
Date solved : Thursday, October 02, 2025 at 09:31:32 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.048 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 16

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

\begin{align*} x(t)&\to \frac {2 t^{3/2}}{3}+1 \end{align*}

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants