44.2.49 problem 52

Internal problem ID [6981]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 52
Date solved : Sunday, March 30, 2025 at 11:32:49 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Maple. Time used: 0.094 (sec). Leaf size: 9

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

\[ y = \frac {x^{4}}{16} \]

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 27

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

\begin{align*} y(x)\to \frac {x^4}{16} \\ y(x)\to \frac {1}{16} \left (x^2-8\right )^2 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*sqrt(y(x)) + Derivative(y(x), x),0) 
ics = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants