26.5.11 problem 14

Internal problem ID [4285]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 14
Date solved : Monday, January 27, 2025 at 08:48:28 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 15

dsolve((6*x+4*y(x)+3)+(3*x+2*y(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.924 (sec). Leaf size: 34

DSolve[(6*x+4*y[x]+3)+(3*x+2*y[x]+2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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