89.10.32 problem 33

Internal problem ID [24525]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 33
Date solved : Thursday, October 02, 2025 at 10:45:44 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -3 y+3+\left (3 x +y+9\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 30

ode:=x-3*y(x)+3+(3*x+y(x)+9)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-x -3\right ) \tan \left (\operatorname {RootOf}\left (-6 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x +3\right )+2 c_1 \right )\right ) \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 54

ode=( x-3*y[x]+3  )+( 3*x+y[x]+9 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [54 \arctan \left (\frac {-3 y(x)+x+3}{y(x)+3 x+9}\right )=9 \log \left (\frac {1}{10} \left (\frac {y(x)^2}{(x+3)^2}+1\right )\right )+18 \log (x+3)+5 c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (3*x + y(x) + 9)*Derivative(y(x), x) - 3*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded