26.2.12 problem Differential equations with Linear Coefficients. Exercise 8.12, page 69

Internal problem ID [6931]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.12, page 69
Date solved : Tuesday, September 30, 2025 at 04:06:27 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.252 (sec). Leaf size: 93

ode:=3*x+2*y(x)+3-(x+2*y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x -2\right ) {\operatorname {RootOf}\left (-1+\left (16 c_1 \,x^{5}+160 c_1 \,x^{4}+640 c_1 \,x^{3}+1280 c_1 \,x^{2}+1280 c_1 x +512 c_1 \right ) \textit {\_Z}^{25}+\left (-80 c_1 \,x^{5}-800 c_1 \,x^{4}-3200 c_1 \,x^{3}-6400 c_1 \,x^{2}-6400 c_1 x -2560 c_1 \right ) \textit {\_Z}^{20}\right )}^{5}}{2}+\frac {3 x}{2}+\frac {9}{2} \]

✓ Mathematica. Time used: 60.063 (sec). Leaf size: 3081

ode=(3*x+2*y[x]+3)-(x+2*y[x]-1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.990 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x - (x + 2*y(x) - 1)*Derivative(y(x), x) + 2*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x + 2 \right )} = C_{1} - \log {\left (\left (- \frac {3}{2} + \frac {y{\left (x \right )} - \frac {3}{2}}{x + 2}\right )^{\frac {4}{5}} \sqrt [5]{1 + \frac {y{\left (x \right )} - \frac {3}{2}}{x + 2}} \right )} \]