30.5.30 problem 30

Internal problem ID [7529]
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 : 30
Date solved : Tuesday, September 30, 2025 at 04:42:15 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} -4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.264 (sec). Leaf size: 36

ode:=-4*x-y(x)-1+(x+y(x)+3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\operatorname {RootOf}\left (-4 \left (3 x -2\right ) c_1 \,\textit {\_Z}^{3}+\textit {\_Z}^{4}-1\right )+\left (6 x -15\right ) c_1}{3 c_1} \]

✓ Mathematica. Time used: 60.186 (sec). Leaf size: 4706

ode=(-4*x-y[x]-1)+(x+y[x]+3)*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(-4*x + (x + y(x) + 3)*Derivative(y(x), x) - y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out