60.1.414 problem 425

Internal problem ID [10428]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 425
Date solved : Sunday, March 30, 2025 at 04:41:43 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Maple. Time used: 0.079 (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 {x +1} \\ y &= x +2+2 \sqrt {x +1} \\ y &= \frac {c_1 \left (c_1 x +c_1 -x \right )}{c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 51

ode=y[x] - (x + y[x])*D[y[x],x] + (1 + x)*D[y[x],x]^2==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