61.22.57 problem 57

Internal problem ID [12382]
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 : 57
Date solved : Tuesday, January 28, 2025 at 07:57:44 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 200

dsolve(y(x)*diff(y(x),x)-y(x)=-10/49*x+2/49*A*(4*x^(1/2)+61*A+12*A^2*x^(-1/2)),y(x), singsol=all)
 

\[ c_{1} -\frac {\left (3 A +\sqrt {x}\right ) 2^{{2}/{3}} \left (\frac {3 A^{2}+16 A \sqrt {x}+5 x -7 y}{6 A^{2}+2 A \sqrt {x}+y}\right )^{{5}/{6}} y}{2 \sqrt {\frac {\left (3 A +\sqrt {x}\right )^{2}}{6 A^{2}+2 A \sqrt {x}+y}}\, \left (\frac {-24 A^{2}-2 A \sqrt {x}+2 x -7 y}{6 A^{2}+2 A \sqrt {x}+y}\right )^{{1}/{3}} \left (6 A^{2}+2 A \sqrt {x}+y\right ) A}-\int _{}^{\frac {6 A \sqrt {x}+2 x -3 y}{12 A^{2}+4 A \sqrt {x}+2 y}}\frac {\left (10 \textit {\_a} +1\right )^{{5}/{6}}}{\sqrt {2 \textit {\_a} +3}\, \left (\textit {\_a} -2\right )^{{1}/{3}}}d \textit {\_a} = 0 \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-y[x]==-10/49*x+2/49*A*(4*x^(1/2)+61*A+12*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
 

Not solved