79.6.1 problem (a)

Internal problem ID [21097]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 1. First order equations: Some integrable cases. Excercises VIII at page 51
Problem number : (a)
Date solved : Thursday, October 02, 2025 at 07:08:14 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }-\sqrt {y^{\prime }-1} \end{align*}

✓ Maple. Time used: 0.075 (sec). Leaf size: 30

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

\begin{align*} y &= \frac {4 x^{2}-1}{4 x} \\ y &= c_1 x -\sqrt {c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to c_1 x-\sqrt {-1+c_1}\\ y(x)&\to -i \end{align*}

✗ Sympy

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

Timed Out