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

Internal problem ID [5796]
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 : Monday, January 27, 2025 at 01:19:09 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*}

✓ Solution by Maple

Time used: 1.202 (sec). Leaf size: 93

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

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

✓ Solution by Mathematica

Time used: 60.108 (sec). Leaf size: 3081

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

Too large to display