29.18.4 problem 480

Internal problem ID [5078]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 480
Date solved : Monday, January 27, 2025 at 10:08:18 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2+2 x +3 y\right ) y^{\prime }&=1-2 x -3 y \end{align*}

✓ Solution by Maple

Time used: 0.027 (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)
 

\[ y \left (x \right ) = -\frac {2 x}{3}+3 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{9}-\frac {7}{9}}}{9}\right )+\frac {7}{3} \]

✓ Solution by Mathematica

Time used: 4.158 (sec). Leaf size: 43

DSolve[(2+2 x+3 y[x])D[y[x],x]==1-2 x-3 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (9 W\left (-e^{-\frac {x}{9}-1+c_1}\right )-2 x+7\right ) \\ y(x)\to \frac {1}{3} (7-2 x) \\ \end{align*}