73.3.38 problem 4.7 (L)

Internal problem ID [15001]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (L)
Date solved : Monday, March 31, 2025 at 01:11:46 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(x),x) = (2+x^(1/2))/(2+y(x)^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ 2 x +\frac {2 x^{{3}/{2}}}{3}-2 y-\frac {2 y^{{3}/{2}}}{3}+c_1 = 0 \]

✓ Mathematica. Time used: 4.257 (sec). Leaf size: 1162

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out