Internal problem ID [9982]
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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable
equations and their solutions
Problem number: 76.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-a^{2} f^{\prime }\relax (x ) f^{\prime \prime }\relax (x )+\frac {\left (f \relax (x )+b \right )^{2} f^{\prime \prime }\relax (x )}{f^{\prime }\relax (x )^{3}}=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==a^2*f'[x]*f''[x]-(f[x]+b)^2/( (f'[x])^3)*f''[x],y[x],x,IncludeSingularSolutions -> True]
Timed out