83.4.23 problem 23

Internal problem ID [19095]
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 : 23
Date solved : Tuesday, January 28, 2025 at 12:55:52 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 19

dsolve((x-y(x)-2)-(2*x-2*y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.060 (sec). Leaf size: 31

DSolve[(x-y[x]-2)-(2*x-2*y[x]-3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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