66.1.35 problem Problem 49

Internal problem ID [13882]
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
Date solved : Tuesday, January 28, 2025 at 06:07:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \end{align*}

✓ Solution by Maple

Time used: 0.067 (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)
 

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

✓ Solution by Mathematica

Time used: 1.006 (sec). Leaf size: 41

DSolve[D[y[x],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*}