Internal problem ID [3226]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 480.
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 (2+2 x +3 y\right ) y^{\prime }-1+2 x +3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((2+2*x+3*y(x))*diff(y(x),x) = 1-2*x-3*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 x}{3}+3 \LambertW \left (\frac {{\mathrm e}^{-\frac {x}{9}} c_{1} {\mathrm e}^{-\frac {7}{9}}}{9}\right )+\frac {7}{3} \]
✓ Solution by Mathematica
Time used: 60.025 (sec). Leaf size: 30
DSolve[(2+2 x+3 y[x])y'[x]==1-2 x-3 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (9 \text {ProductLog}\left (-e^{-\frac {x}{9}-1+c_1}\right )-2 x+7\right ) \\ \end{align*}