81.1.31 problem 2-29

Internal problem ID [21476]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-29
Date solved : Thursday, October 02, 2025 at 07:39:29 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.138 (sec). Leaf size: 213

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

\[ y = \frac {\left (-4 x -1\right ) {\operatorname {RootOf}\left (-1+\left (442368 c_1 \,x^{7}+774144 c_1 \,x^{6}+580608 c_1 \,x^{5}+241920 c_1 \,x^{4}+60480 c_1 \,x^{3}+9072 c_1 \,x^{2}+756 c_1 x +27 c_1 \right ) \textit {\_Z}^{49}+\left (-3096576 c_1 \,x^{7}-5419008 c_1 \,x^{6}-4064256 c_1 \,x^{5}-1693440 c_1 \,x^{4}-423360 c_1 \,x^{3}-63504 c_1 \,x^{2}-5292 c_1 x -189 c_1 \right ) \textit {\_Z}^{42}+\left (7225344 c_1 \,x^{7}[phone] c_1 \,x^{6}+9483264 c_1 \,x^{5}+3951360 c_1 \,x^{4}+987840 c_1 \,x^{3}+148176 c_1 \,x^{2}+12348 c_1 x +441 c_1 \right ) \textit {\_Z}^{35}+\left (-5619712 c_1 \,x^{7}-9834496 c_1 \,x^{6}-7375872 c_1 \,x^{5}-3073280 c_1 \,x^{4}-768320 c_1 \,x^{3}-115248 c_1 \,x^{2}-9604 c_1 x -343 c_1 \right ) \textit {\_Z}^{28}\right )}^{7}}{4}+2 x +1 \]

✓ Mathematica. Time used: 0.072 (sec). Leaf size: 92

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

\[ \text {Solve}\left [\frac {1}{30} \left (\log \left (\frac {45 x^2-45 y(x)^2+(75 x+63) y(x)-22 x-19}{3 (5 x+1)^2}\right )+2 \log (15 x+3)\right )=\frac {\text {arctanh}\left (\frac {1-\frac {6 (5 x+1)}{-3 y(x)+2 x+2}}{\sqrt {61}}\right )}{15 \sqrt {61}}+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out