Internal problem ID [12157]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (4 y+2 x +3\right ) y^{\prime }-2 y=x +1} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = -\frac {x}{2}+\frac {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{5+8 x}\right )}{8}-\frac {5}{8} \]
✓ Solution by Mathematica
Time used: 6.325 (sec). Leaf size: 39
DSolve[(4*y[x]+2*x+3)*y'[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*}