Internal problem ID [11706]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y-\left (6 x -2 y-3\right ) y^{\prime }=-3 x -1} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{5 x -4-5 c_{1}}\right )}{2}+3 x -2 \]
✓ Solution by Mathematica
Time used: 3.097 (sec). Leaf size: 35
DSolve[(3*x-y[x]+1)-(6*x-2*y[x]-3)*y'[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*}