83.4.1 problem 1

Internal problem ID [19073]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 12:51:54 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 18

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

\[ y \left (x \right ) = -\operatorname {LambertW}\left (-{\mathrm e}^{-2 x} c_{1} \right )-x \]

✓ Solution by Mathematica

Time used: 3.890 (sec). Leaf size: 30

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

\begin{align*} y(x)\to -x-W\left (-e^{-2 x-1+c_1}\right ) \\ y(x)\to -x \\ \end{align*}