66.1.25 problem Problem 36

Internal problem ID [13872]
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 36
Date solved : Tuesday, January 28, 2025 at 06:06:35 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.914 (sec). Leaf size: 35

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

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