Internal problem ID [12449]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y-\left (4 y+2 x +3\right ) y^{\prime }=-x -1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 20
dsolve((x+2*y(x)+1)-(2*x+4*y(x)+3)*diff(y(x),x)=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: 6.228 (sec). Leaf size: 39
DSolve[(x+2*y[x]+1)-(2*x+4*y[x]+3)*y'[x]==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*}