75.9.10 problem 229

Internal problem ID [16776]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number : 229
Date solved : Monday, March 31, 2025 at 03:16:58 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

\begin{align*} x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 47

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

\begin{align*} y(x)\to c_1 x-\frac {1}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 i \sqrt {x} \\ y(x)\to 2 i \sqrt {x} \\ \end{align*}

✗ Sympy

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

Timed Out