85.13.6 problem 6

Internal problem ID [22512]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 40
Problem number : 6
Date solved : Thursday, October 02, 2025 at 08:44:11 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x +3 y+1}{3 x -2 y-5} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 68

ode=D[y[x],x]==(2*x+3*y[x]+1)/(3*x-2*y[x]-5); 
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: 1.418 (sec). Leaf size: 37

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

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