61.22.4 problem 4

Internal problem ID [12329]
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 : 4
Date solved : Tuesday, January 28, 2025 at 07:54:31 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 120

dsolve(y(x)*diff(y(x),x)-y(x)=2*A*(x^(1/2)+4*A+3*A^2*x^(-1/2)),y(x), singsol=all)
 

\[ \frac {4 \sqrt {-\frac {A^{2}}{y}}\, \operatorname {arctanh}\left (\frac {\sqrt {-\frac {A^{2}}{y}}\, \left (3 A +\sqrt {x}\right )}{\sqrt {\frac {-3 A^{2}-4 A \sqrt {x}-x +y}{y}}\, A}\right )-\sqrt {\frac {-6 A^{2}-8 A \sqrt {x}-2 x +2 y}{y}}\, \sqrt {2}+c_{1} \sqrt {-\frac {A^{2}}{y}}}{\sqrt {-\frac {A^{2}}{y}}} = 0 \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-y[x]==2*A*(x^(1/2)+4*A+3*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
 

Not solved