87.2.4 problem 4

Internal problem ID [23239]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:25:04 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

ode=D[y[x],x]==y[x]^(1/2); 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants