61.22.12 problem 12

Internal problem ID [12337]
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 : 12
Date solved : Tuesday, January 28, 2025 at 02:47:29 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=\frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (m +3\right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (m +3\right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=2*(m-1)/(m-3)^2+2*A/(m-3)^2*(m*(m+3)*x^(1/2)+(4*m^2+3*m+9)*A+3*m*(m+3)*A^2*x^(-1/2)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-y[x]==2*(m-1)/(m-3)^2+2*A/(m-3)^2*(m*(m+3)*x^(1/2)+(4*m^2+3*m+9)*A+3*m*(m+3)*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
 

Not solved