69.11.10 problem 269

Internal problem ID [18148]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 269
Date solved : Thursday, October 02, 2025 at 03:02:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 839

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

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

✓ Mathematica. Time used: 60.871 (sec). Leaf size: 2409

ode=y[x]==D[y[x],x]^2-x*D[y[x],x]+x^2/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(x*Derivative(y(x), x) - x + y(x) - Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out