83.4.9 problem 9

Internal problem ID [19081]
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 : 9
Date solved : Tuesday, January 28, 2025 at 12:52:28 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+1-\left (2 x +2 y+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 23

dsolve((x+y(x)+1)-(2*x+2*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-9 x -4+9 c_{1}}\right )}{6}-x -\frac {2}{3} \]

✓ Solution by Mathematica

Time used: 3.921 (sec). Leaf size: 39

DSolve[(x+y[x]+1)-(2*x+2*y[x]+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{6} \left (-W\left (-e^{-9 x-1+c_1}\right )-6 x-4\right ) \\ y(x)\to -x-\frac {2}{3} \\ \end{align*}