29.18.1 problem 477

Internal problem ID [5075]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 477
Date solved : Monday, January 27, 2025 at 10:08:09 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 19

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

\[ y \left (x \right ) = -2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x^{2}}{12}-\frac {c_{1}}{6}}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 19.238 (sec). Leaf size: 64

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

\begin{align*} y(x)\to -2 W\left (-\frac {1}{2} \sqrt {e^{-\frac {x^2}{6}-c_1}}\right ) \\ y(x)\to -2 W\left (\frac {1}{2} \sqrt {e^{-\frac {x^2}{6}-c_1}}\right ) \\ y(x)\to 0 \\ \end{align*}