Internal problem ID [10657]
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: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-y=A +B \,{\mathrm e}^{-\frac {2 x}{A}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 76
dsolve(y(x)*diff(y(x),x)-y(x)=A+B*exp(-2*x/A),y(x), singsol=all)
\[ c_{1} -2 \arctan \left (\frac {y \left (x \right )+A}{y \left (x \right ) \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y \left (x \right )+A \right )^{2}}{y \left (x \right )^{2}}}}\right ) A -2 \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y \left (x \right )+A \right )^{2}}{y \left (x \right )^{2}}}\, y \left (x \right ) = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==A+B*Exp[-2*x/A],y[x],x,IncludeSingularSolutions -> True]
Not solved