66.1.46 problem Problem 60

Internal problem ID [13893]
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 60
Date solved : Tuesday, January 28, 2025 at 06:07:43 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 20

dsolve((4*y(x)+2*x+3)*diff(y(x),x)-2*y(x)-x-1=0,y(x), singsol=all)
 

\[ y = -\frac {x}{2}+\frac {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{5+8 x}\right )}{8}-\frac {5}{8} \]

✓ Solution by Mathematica

Time used: 4.008 (sec). Leaf size: 39

DSolve[(4*y[x]+2*x+3)*D[y[x],x]-2*y[x]-x-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (W\left (-e^{8 x-1+c_1}\right )-4 x-5\right ) \\ y(x)\to \frac {1}{8} (-4 x-5) \\ \end{align*}