Internal problem ID [10714]
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: 65.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y y^{\prime }-y=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{\frac {1}{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{\frac {1}{3}}}-\frac {A \,B^{3}}{x^{\frac {2}{3}}}\right )}{75}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 3187
dsolve(y(x)*diff(y(x),x)-y(x)=-6/25*x+4/75*B^2*((2-A)*x^(1/3)-3/2*B*(2*A+1)+B^2*(1-3*A)*x^(-1/3)-A*B^3*x^(-2/3)),y(x), singsol=all)
\[ \text {Expression too large to display} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==-6/25*x+4/75*B^2*((2-A)*x^(1/3)-3/2*B*(2*A+1)+B^2*(1-3*A)*x^(-1/3)-A*B^3*x^(-2/3)),y[x],x,IncludeSingularSolutions -> True]
Not solved