60.1.372 problem 381

Internal problem ID [10386]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 381
Date solved : Sunday, March 30, 2025 at 04:34:20 PM
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: 60.184 (sec). Leaf size: 954

ode=y[x] - 2*x*D[y[x],x] + D[y[x],x]^2==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