48.1.5 problem Example 3.5

Internal problem ID [7506]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.5
Date solved : Sunday, March 30, 2025 at 12:11:24 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 59

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

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

✓ Sympy. Time used: 2.422 (sec). Leaf size: 34

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

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