83.7.5 problem 5

Internal problem ID [21953]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. VIII at page 53
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:19:24 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.085 (sec). Leaf size: 57

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

\[ y = \frac {3}{2}+\frac {\sqrt {3}\, \left (x -1\right ) \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (\left (x -1\right )^{2} \sec \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (3\right )+2 \sqrt {3}\, c_1 +4 \textit {\_Z} \right )\right )}{2}-\frac {x}{2} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 79

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

\[ \text {Solve}\left [32 \sqrt {3} \arctan \left (\frac {-4 y(x)+x+3}{\sqrt {3} (2 y(x)+3 x-5)}\right )=3 \left (8 \log \left (\frac {4 \left (x^2+y(x)^2+(x-3) y(x)-3 x+3\right )}{7 (x-1)^2}\right )+16 \log (x-1)+7 c_1\right ),y(x)\right ] \]

✓ Sympy. Time used: 3.537 (sec). Leaf size: 61

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

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