60.1.209 problem 213

Internal problem ID [10223]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 213
Date solved : Sunday, March 30, 2025 at 03:32:25 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.800 (sec). Leaf size: 66

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

\[ -\frac {\ln \left (\frac {y^{2}+\left (-x +3\right ) y-x^{2}+x +1}{\left (x -1\right )^{2}}\right )}{2}-\frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (-3-2 y+x \right ) \sqrt {5}}{5 x -5}\right )}{5}-\ln \left (x -1\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 71

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

\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {x^2-y(x)^2+(x-3) y(x)-x-1}{(x-1)^2}\right )+\log (1-x)=\frac {\text {arctanh}\left (\frac {y(x)+2 x-1}{\sqrt {5} (y(x)+1)}\right )}{\sqrt {5}}+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out