Internal problem ID [5244]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (2 x +2 y+1\right ) y^{\prime }=-x -1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve((x+y(x)+1)+(2*x+2*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{-\operatorname {LambertW}\left (2 \,{\mathrm e}^{-c_{1}} {\mathrm e}^{x}\right )+x -c_{1}}-x \]
✓ Solution by Mathematica
Time used: 4.251 (sec). Leaf size: 30
DSolve[(x+y[x]+1)+(2*x+2*y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-2 x+W\left (-e^{x-1+c_1}\right )\right ) y(x)\to -x \end{align*}