Internal problem ID [3747]
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`]]
\[ \boxed {3 \left (x +2 y\right ) y^{\prime }+2 y=1-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-{\mathrm e}^{-\frac {x}{6}} {\mathrm e}^{-1} {\mathrm e}^{\frac {c_{1}}{6}}\right )-\frac {x}{6}-1+\frac {c_{1}}{6}}-1-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 4.134 (sec). Leaf size: 39
DSolve[3(x+2 y[x])y'[x]==1-x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -W\left (-e^{-\frac {x}{6}-1+c_1}\right )-\frac {x}{2}-1 y(x)\to -\frac {x}{2}-1 \end{align*}