29.17.7 problem 466

Internal problem ID [5064]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 466
Date solved : Monday, January 27, 2025 at 10:07:21 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 4.103 (sec). Leaf size: 43

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

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