Internal problem ID [3720]
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`]]
\[ \boxed {\left (1+x +2 y\right ) y^{\prime }-2 y=-1+x} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 21
dsolve((1+x+2*y(x))*diff(y(x),x)+1-x-2*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2}+\frac {2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {9 x}{4}} {\mathrm e}^{-\frac {1}{4}} c_{1}}{4}\right )}{3}+\frac {1}{6} \]
✓ Solution by Mathematica
Time used: 5.086 (sec). Leaf size: 43
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 W\left (-e^{\frac {9 x}{4}-1+c_1}\right )-3 x+1\right ) y(x)\to \frac {1}{6} (1-3 x) \end{align*}