15.8.9 problem 9

Internal problem ID [3012]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:07:47 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 21

dsolve((x-3*y(x))=(3*y(x)-x+2)*diff(y(x),x),y(x), singsol=all)
 

\[ y = \frac {x}{3}+\frac {\operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{\frac {1}{3}-\frac {8 x}{3}}}{3}\right )}{2}-\frac {1}{6} \]

✓ Solution by Mathematica

Time used: 4.917 (sec). Leaf size: 43

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

\begin{align*} y(x)\to \frac {1}{6} \left (3 W\left (-e^{-\frac {8 x}{3}-1+c_1}\right )+2 x-1\right ) \\ y(x)\to \frac {1}{6} (2 x-1) \\ \end{align*}