61.22.76 problem 76

Internal problem ID [12401]
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 : 76
Date solved : Tuesday, January 28, 2025 at 02:58:29 AM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=a^2*diff(f(x),x)*diff(f(x),x$2)-(f(x)+b)^2/( diff(f(x),x)^3)*diff(f(x),x$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]==a^2*D[ f[x],x]*D[ f[x],{x,2}]-(f[x]+b)^2/( (D[ f[x],x])^3)*D[ f[x],{x,2}],y[x],x,IncludeSingularSolutions -> True]
 

Not solved