Internal problem ID [10798]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {3 x -4 y-2}{3 x -4 y-3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x)=(3*x-4*y(x)-2)/(3*x-4*y(x)-3),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 x}{4}+\operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {1}{4}} {\mathrm e}^{\frac {x}{4}} c_{1}}{4}\right )+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 3.882 (sec). Leaf size: 41
DSolve[y'[x]==(3*x-4*y[x]-2)/(3*x-4*y[x]-3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (-e^{\frac {x}{4}-1+c_1}\right )+\frac {3 x}{4}+\frac {1}{4} \\ y(x)\to \frac {1}{4} (3 x+1) \\ \end{align*}