23.2.150 problem 153

Internal problem ID [5505]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 153
Date solved : Tuesday, September 30, 2025 at 12:45:58 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 42

ode:=x^2*diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+1+y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {4 x^{2}-1}{4 x} \\ y &= c_1 x -\sqrt {c_1 -1} \\ y &= c_1 x +\sqrt {c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.901 (sec). Leaf size: 66

ode=x^2 (D[y[x],x])^2-(1+2 x y[x])D[y[x],x]+1+y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x+e^{-2 c_1} x+e^{-c_1}\\ y(x)&\to x+\frac {1}{4} e^{-2 c_1} x+\frac {e^{-c_1}}{2}\\ y(x)&\to x\\ y(x)&\to x-\frac {1}{4 x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 - (2*x*y(x) + 1)*Derivative(y(x), x) + y(x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out