60.7.203 problem 1828 (book 6.237)

Internal problem ID [11753]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1828 (book 6.237)
Date solved : Sunday, March 30, 2025 at 09:13:35 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 4.618 (sec). Leaf size: 1364

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

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

✗ Mathematica

ode=D[y[x],x] - 2*a*x*D[y[x],{x,2}] + a^2*D[y[x],{x,2}]^2 == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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