29.16.5 problem 448

Internal problem ID [5046]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 448
Date solved : Monday, January 27, 2025 at 10:05:35 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 22

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

\[ y(x)\to W\left (-2 c_1 e^{-2 (x+2)}\right )+2 x+4 \]