85.10.5 problem 4

Internal problem ID [22492]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 37
Problem number : 4
Date solved : Sunday, October 12, 2025 at 05:52:29 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 50

ode:=diff(U(s),s) = (U(s)+1)/(s^(1/2)+(s*U(s))^(1/2)); 
dsolve(ode,U(s), singsol=all);
 

\[ \frac {2 s -\ln \left (U+1\right ) \sqrt {s}+2 \arctan \left (\frac {\sqrt {s U}}{\sqrt {s}}\right ) \sqrt {s}+c_1 \sqrt {s}-2 \sqrt {s U}}{\sqrt {s}} = 0 \]

✓ Mathematica. Time used: 0.443 (sec). Leaf size: 45

ode=D[U[s],s]== (U[s]+1)/( Sqrt[s]+Sqrt[s*U[s]] ); 
ic={}; 
DSolve[{ode,ic},U[s],s,IncludeSingularSolutions->True]
 

\begin{align*} U(s)&\to \text {InverseFunction}\left [-2 \arctan \left (\sqrt {\text {$\#$1}}\right )+2 \sqrt {\text {$\#$1}}+\log (\text {$\#$1}+1)\&\right ]\left [2 \sqrt {s}+c_1\right ]\\ U(s)&\to -1 \end{align*}

✗ Sympy

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

Timed Out