49.21.15 problem 5(c)

Internal problem ID [7745]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 5(c)
Date solved : Monday, January 27, 2025 at 03:11:55 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y+1}{2 x +2 y-1} \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 3.857 (sec). Leaf size: 32

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

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