30.5.32 problem 32

Internal problem ID [7531]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 32
Date solved : Tuesday, September 30, 2025 at 04:42:57 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.354 (sec). Leaf size: 58

ode:=2*x-y(x)+4+(x-2*y(x)-2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-1+c_1 \left (3 x +2\right ) \operatorname {RootOf}\left (-1+\textit {\_Z}^{4}+\left (6 c_1 x +20 c_1 \right ) \textit {\_Z}^{3}\right )^{3}}{3 \operatorname {RootOf}\left (-1+\textit {\_Z}^{4}+\left (6 c_1 x +20 c_1 \right ) \textit {\_Z}^{3}\right )^{3} c_1} \]

✓ Mathematica. Time used: 60.182 (sec). Leaf size: 4715

ode=(2*x-y[x]+4)+(x-2*y[x]-2)*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) - 2)*Derivative(y(x), x) - y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out