29.17.11 problem 470

Internal problem ID [5068]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 470
Date solved : Monday, January 27, 2025 at 10:07:33 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 23

dsolve((1-4*x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{4-25 x +25 c_{1}}\right )}{10}+\frac {2}{5}-2 x \]

✓ Solution by Mathematica

Time used: 3.126 (sec). Leaf size: 39

DSolve[(1-4 x-2 y[x])D[y[x],x]+2 x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{10} W\left (-e^{-25 x-1+c_1}\right )-2 x+\frac {2}{5} \\ y(x)\to \frac {2}{5}-2 x \\ \end{align*}