Internal problem ID [3239]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 493.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {3 \left (x +2 y\right ) y^{\prime }-1+x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-{\mathrm e}^{-1} {\mathrm e}^{-\frac {x}{6}} {\mathrm e}^{\frac {c_{1}}{6}}\right )-1-\frac {x}{6}+\frac {c_{1}}{6}}-1-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 28
DSolve[3(x+2 y[x])y'[x]==1-x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ProductLog}\left (-e^{-\frac {x}{6}-1+c_1}\right )-\frac {x}{2}-1 \\ \end{align*}