87.6.17 problem 20

Internal problem ID [23334]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 53
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:37:54 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.757 (sec). Leaf size: 68

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

\[ -\frac {\ln \left (\frac {y^{2}+\left (-3 x -2\right ) y+x^{2}+23 x -79}{\left (x -8\right )^{2}}\right )}{2}-\frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (-3 x -2+2 y\right ) \sqrt {5}}{5 x -40}\right )}{5}-\ln \left (x -8\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 77

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

\[ \text {Solve}\left [\frac {\text {arctanh}\left (\frac {y(x)-4 x+19}{\sqrt {5} (-y(x)+2 x-3)}\right )}{\sqrt {5}}+\frac {1}{2} \log \left (-\frac {x^2+y(x)^2-(3 x+2) y(x)+23 x-79}{(x-8)^2}\right )+\log (8-x)=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out