61.22.37 problem 37

Internal problem ID [12362]
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 : 37
Date solved : Tuesday, January 28, 2025 at 07:57:07 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=2 A^{2}-A \sqrt {x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 228

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

\[ \frac {\left (-2 A +\sqrt {x}\right ) \operatorname {BesselK}\left (1, -\sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\right )+\operatorname {BesselK}\left (0, -\sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\right ) \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\, A +c_{1} \left (\left (-2 A +\sqrt {x}\right ) \operatorname {BesselI}\left (1, \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\right )+A \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\, \operatorname {BesselI}\left (0, \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\right )\right )}{\left (-2 A +\sqrt {x}\right ) \operatorname {BesselI}\left (1, \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\right )+A \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\, \operatorname {BesselI}\left (0, \sqrt {-\frac {2 A \sqrt {x}-x +y}{A^{2}}}\right )} = 0 \]

✗ Solution by Mathematica

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

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

Not solved