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 : Monday, January 27, 2025 at 03:02:59 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*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 59

DSolve[D[y[x],x]==(x+y[x]-1)/(x-y[x]+3),y[x],x,IncludeSingularSolutions -> True]
 

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