23.2.128 problem 130

Internal problem ID [5483]
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 : 130
Date solved : Tuesday, September 30, 2025 at 12:45:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Maple. Time used: 0.077 (sec). Leaf size: 45

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

\begin{align*} y &= x +2-2 \sqrt {1+x} \\ y &= x +2+2 \sqrt {1+x} \\ y &= \frac {c_1 \left (c_1 x +c_1 -x \right )}{c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 51

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

\begin{align*} y(x)&\to c_1 \left (x+\frac {c_1}{-1+c_1}\right )\\ y(x)&\to x-2 \sqrt {x+1}+2\\ y(x)&\to x+2 \sqrt {x+1}+2 \end{align*}

✗ Sympy

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

Timed Out