19.3.1 problem 9

Internal problem ID [3544]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:41:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

dsolve((3*x-y(x))*diff(y(x),x)=3*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.638 (sec). Leaf size: 25

DSolve[(3*x-y[x])*D[y[x],x]==3*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 x}{W\left (-3 e^{-c_1} x\right )} \\ y(x)\to 0 \\ \end{align*}