Internal problem ID [10650]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 1, section 1.3. Abel Equations of the Second Kind. Form \(y y'-y=f(x)\). subsection 1.3.1-2.
Solvable equations and their solutions
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y y^{\prime }-y=A} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(y(x)*diff(y(x),x)-y(x)=A,y(x), singsol=all)
\[ y \left (x \right ) = -A \left (\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {-A -c_{1} -x}{A}}}{A}\right )+1\right ) \]
✓ Solution by Mathematica
Time used: 60.032 (sec). Leaf size: 28
DSolve[y[x]*y'[x]-y[x]==A,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -A \left (1+W\left (-\frac {e^{-\frac {A+x+c_1}{A}}}{A}\right )\right ) \]