Internal problem ID [3223]
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]
Solve \begin {gather*} \boxed {3 \left (-y+2\right ) y^{\prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(3*(2-y(x))*diff(y(x),x)+x*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{-\frac {x^{2}}{12}-\frac {c_{1}}{6}}}{2}\right )-\frac {x^{2}}{12}-\frac {c_{1}}{6}} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 59
DSolve[3(2-y[x])y'[x]+x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \text {ProductLog}\left (-\frac {1}{2} \sqrt {e^{-\frac {x^2}{6}-c_1}}\right ) \\ y(x)\to -2 \text {ProductLog}\left (\frac {1}{2} \sqrt {e^{-\frac {x^2}{6}-c_1}}\right ) \\ \end{align*}