Internal problem ID [3212]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 466.
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 {\left (x +2 y+1\right ) y^{\prime }+1-x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((1+x+2*y(x))*diff(y(x),x)+1-x-2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2}+\frac {2 \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{4}} {\mathrm e}^{\frac {9 x}{4}} c_{1}}{4}\right )}{3}+\frac {1}{6} \]
✓ Solution by Mathematica
Time used: 60.038 (sec). Leaf size: 30
DSolve[(1+x+2 y[x])y'[x]+1-x-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (4 \text {ProductLog}\left (-e^{\frac {9 x}{4}-1+c_1}\right )-3 x+1\right ) \\ \end{align*}