Internal problem ID [9915]
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: 9.
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 \left ({\mathrm e}^{\frac {2 x}{A}}-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 82
dsolve(y(x)*diff(y(x),x)-y(x)=A*(exp(2*x/A)-1),y(x), singsol=all)
\[ c_{1}+2 \arctan \left (\frac {A -y \relax (x )}{y \relax (x ) \sqrt {\frac {A^{2} {\mathrm e}^{\frac {2 x}{A}}-\left (A -y \relax (x )\right )^{2}}{y \relax (x )^{2}}}}\right ) A +2 \sqrt {\frac {A^{2} {\mathrm e}^{\frac {2 x}{A}}-\left (A -y \relax (x )\right )^{2}}{y \relax (x )^{2}}}\, y \relax (x ) = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==A*(Exp[2*x/A]-1),y[x],x,IncludeSingularSolutions -> True]
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