54.1.406 problem 417

Internal problem ID [11720]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 417
Date solved : Tuesday, September 30, 2025 at 10:14:25 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 35

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

\begin{align*} y &= -2 \sqrt {a x} \\ y &= 2 \sqrt {a x} \\ y &= \frac {c_1^{2} x +a}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to \frac {a}{c_1}+c_1 x\\ y(x)&\to \text {Indeterminate}\\ y(x)&\to -2 \sqrt {a} \sqrt {x}\\ y(x)&\to 2 \sqrt {a} \sqrt {x} \end{align*}

✗ Sympy

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

Timed Out