29.18.3 problem 479

Internal problem ID [5077]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 479
Date solved : Monday, January 27, 2025 at 10:08:15 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 21

dsolve((4-x-3*y(x))*diff(y(x),x)+3-x-3*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x}{3}-\frac {\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {4 x}{3}+\frac {5}{3}}}{3}\right )}{2}+\frac {5}{6} \]

✓ Solution by Mathematica

Time used: 4.127 (sec). Leaf size: 43

DSolve[(4-x-3 y[x])D[y[x],x]+3-x-3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{6} \left (-3 W\left (-e^{\frac {4 x}{3}-1+c_1}\right )-2 x+5\right ) \\ y(x)\to \frac {1}{6} (5-2 x) \\ \end{align*}