83.9.9 problem 9

Internal problem ID [21967]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. X at page 57
Problem number : 9
Date solved : Thursday, October 02, 2025 at 08:20:24 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.447 (sec). Leaf size: 53

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

\[ y = \frac {c_1 \operatorname {RootOf}\left (-1+\textit {\_Z}^{4}+\left (2 c_1 x +2 c_1 \right ) \textit {\_Z}^{3}\right )^{3} x -1}{\operatorname {RootOf}\left (-1+\textit {\_Z}^{4}+\left (2 c_1 x +2 c_1 \right ) \textit {\_Z}^{3}\right )^{3} c_1} \]

✓ Mathematica. Time used: 60.179 (sec). Leaf size: 4389

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

Too large to display

✗ Sympy

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

Timed Out