Internal problem ID [2666]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (3 x -y\right ) y^{\prime }-3 y=0} \]
✓ 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)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {LambertW}\left (-3 x \,{\mathrm e}^{-3 c_{1}}\right )+3 c_{1}} \]
✓ Solution by Mathematica
Time used: 6.103 (sec). Leaf size: 25
DSolve[(3*x-y[x])*y'[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*}