43.21.8 problem 3(b)

Internal problem ID [9024]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 3(b)
Date solved : Tuesday, September 30, 2025 at 06:01:40 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 5

ode:=diff(y(x),x) = 2*y(x)^(1/2); 
ic:=[y(x__0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

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

ode=D[y[x],x]==2*Sqrt[y[x]]; 
ic={y[x0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*sqrt(y(x)) + Derivative(y(x), x),0) 
ics = {y(x__0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} - 2 x x^{0} + \left (x^{0}\right )^{2} \]