Internal problem ID [3731]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 477.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 \left (2-y\right ) y^{\prime }+y x=0} \]
✓ Solution by Maple
Time used: 0.016 (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: 24.428 (sec). Leaf size: 64
DSolve[3(2-y[x])y'[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*}