78.8.3 problem 3

Internal problem ID [18130]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 3
Date solved : Monday, March 31, 2025 at 05:12:42 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 31

ode:=2*x+3*y(x)+1+(2*y(x)-3*x+5)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -1-\tan \left (\operatorname {RootOf}\left (3 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_1 \right )\right ) \left (x -1\right ) \]

✓ Mathematica. Time used: 0.061 (sec). Leaf size: 68

ode=(2*x+3*y[x]+1)+(2*y[x]-3*x+5)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [54 \arctan \left (\frac {3 y(x)+2 x+1}{2 y(x)-3 x+5}\right )+18 \log \left (\frac {4 \left (x^2+y(x)^2+2 y(x)-2 x+2\right )}{13 (x-1)^2}\right )+36 \log (x-1)+13 c_1=0,y(x)\right ] \]

✓ Sympy. Time used: 2.163 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (-3*x + 2*y(x) + 5)*Derivative(y(x), x) + 3*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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