66.1.51 problem Problem 65

Internal problem ID [13827]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 65
Date solved : Monday, March 31, 2025 at 08:14:27 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 603

ode:=diff(y(x),x)^2-2*x*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 60.179 (sec). Leaf size: 954

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

NotImplementedError : The given ODE -x - sqrt(x**2 - y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method