61.22.49 problem 49

Internal problem ID [12374]
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 : 49
Date solved : Tuesday, January 28, 2025 at 07:57:24 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 196

dsolve(y(x)*diff(y(x),x)-y(x)=2*x+2*A*(10*x^(1/2)+31*A+30*A^2*x^(-1/2)),y(x), singsol=all)
 

\[ c_{1} -\frac {\left (3 A +\sqrt {x}\right ) 2^{{1}/{3}} \left (\frac {12 A^{2}+10 A \sqrt {x}+2 x -y}{6 A^{2}+2 A \sqrt {x}+y}\right )^{{1}/{3}} \left (\frac {15 A^{2}+8 A \sqrt {x}+x +y}{6 A^{2}+2 A \sqrt {x}+y}\right )^{{1}/{6}} y}{4 \sqrt {\frac {\left (3 A +\sqrt {x}\right )^{2}}{6 A^{2}+2 A \sqrt {x}+y}}\, \left (6 A^{2}+2 A \sqrt {x}+y\right ) A}-\int _{}^{\frac {6 A \sqrt {x}+2 x -3 y}{12 A^{2}+4 A \sqrt {x}+2 y}}\frac {\left (\textit {\_a} +1\right )^{{1}/{3}} \left (2 \textit {\_a} +5\right )^{{1}/{6}}}{\sqrt {2 \textit {\_a} +3}}d \textit {\_a} = 0 \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-y[x]==2*x+2*A*(10*x^(1/2)+31*A+30*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
 

Not solved