Internal problem ID [9972]
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: 66.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-\frac {3 x}{4}+\frac {3 A \,x^{\frac {1}{3}}}{2}-\frac {3 A^{2}}{4 x^{\frac {1}{3}}}+\frac {27 A^{4}}{625 x^{\frac {5}{3}}}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-y(x)=3/4*x-3/2*A*x^(1/3)+3/4*A^2*x^(-1/3)-27/625*A^4*x^(-5/3),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]==3/4*x-3/2*A*x^(1/3)+3/4*A^2*x^(-1/3)-27/625*A^4*x^(-5/3),y[x],x,IncludeSingularSolutions -> True]
Not solved