73.1.11 problem 2 (v)

Internal problem ID [19784]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 2 (v)
Date solved : Thursday, October 02, 2025 at 04:43:24 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=2 \sqrt {x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 9

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

\[ x = \left (t +1\right )^{2} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 10

ode=D[x[t],t]==2*Sqrt[x[t]]; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*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