75.9.4 problem 223

Internal problem ID [16770]
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 : 223
Date solved : Monday, March 31, 2025 at 03:16:44 PM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.059 (sec). Leaf size: 1807

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

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

✓ Mathematica. Time used: 141.713 (sec). Leaf size: 21579

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

Too large to display

✗ Sympy

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

Timed Out