61.22.53 problem 53

Internal problem ID [12378]
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 : 53
Date solved : Tuesday, January 28, 2025 at 07:57:39 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=-\frac {12 x}{49}+A \sqrt {x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 133

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

\[ \frac {\left (\left (\frac {4 \sqrt {3}\, \left (x -\frac {7 y}{4}\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {7}{6}\right ], \left [\frac {3}{2}\right ], \frac {3 \left (-4 x +7 y\right )^{2}}{196 x^{{3}/{2}} A}\right )}{7}+\sqrt {x}\, \sqrt {A \sqrt {x}}\, c_{1} \right ) 196^{{1}/{6}} \left (\frac {A \,x^{{3}/{2}}-\frac {12 \left (x -\frac {7 y}{4}\right )^{2}}{49}}{x^{{3}/{2}} A}\right )^{{1}/{6}}-7 \,14^{{1}/{3}} A \sqrt {3}\, \sqrt {x}\right ) 196^{{5}/{6}}}{196 \sqrt {x}\, \sqrt {A \sqrt {x}}\, \left (\frac {A \,x^{{3}/{2}}-\frac {12 \left (x -\frac {7 y}{4}\right )^{2}}{49}}{x^{{3}/{2}} A}\right )^{{1}/{6}}} = 0 \]

✗ Solution by Mathematica

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

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

Not solved