61.22.9 problem 9

Internal problem ID [12334]
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 : 9
Date solved : Tuesday, January 28, 2025 at 07:54:43 PM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 82

dsolve(y(x)*diff(y(x),x)-y(x)=A*(exp(2*x/A)-1),y(x), singsol=all)
 

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

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-y[x]==A*(Exp[2*x/A]-1),y[x],x,IncludeSingularSolutions -> True]
 

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