61.22.8 problem 8

Internal problem ID [12333]
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. subsection 1.3.1-2. Solvable equations and their solutions
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 07:54:41 PM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 76

dsolve(y(x)*diff(y(x),x)-y(x)=A+B*exp(-2*x/A),y(x), singsol=all)
 

\[ c_{1} -2 A \arctan \left (\frac {y+A}{y \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y+A \right )^{2}}{y^{2}}}}\right )-2 \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y+A \right )^{2}}{y^{2}}}\, y = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]-y[x]==A+B*Exp[-2*x/A],y[x],x,IncludeSingularSolutions -> True]
 

Not solved