64.7.8 problem 8

Internal problem ID [13382]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:36:19 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 23

dsolve((3*x-y(x)+1)-(6*x-2*y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{5 x -4-5 c_{1}}\right )}{2}+3 x -2 \]

✓ Solution by Mathematica

Time used: 0.856 (sec). Leaf size: 35

DSolve[(3*x-y[x]+1)-(6*x-2*y[x]-3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} W\left (-e^{5 x-1+c_1}\right )+3 x-2 \\ y(x)\to 3 x-2 \\ \end{align*}