Internal problem ID [9914]
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]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-A -B \,{\mathrm e}^{-\frac {2 x}{A}}=0} \end {gather*}
✓ 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)
\[ c_{1}-2 \arctan \left (\frac {y \relax (x )+A}{y \relax (x ) \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y \relax (x )+A \right )^{2}}{y \relax (x )^{2}}}}\right ) A -2 \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y \relax (x )+A \right )^{2}}{y \relax (x )^{2}}}\, y \relax (x ) = 0 \]
✗ 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