Internal problem ID [10709]
Internal file name [OUTPUT/9657_Monday_June_06_2022_03_18_13_PM_97476693/index.tex]
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: 61.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[_rational, [_Abel, `2nd type`, `class B`]]
Unable to solve or complete the solution.
\[ \boxed {y y^{\prime }-y=-\frac {3 x}{16}+\frac {A}{x^{\frac {1}{3}}}+\frac {B}{x^{\frac {5}{3}}}} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & -16 y y^{\prime } x^{\frac {5}{3}}+16 y x^{\frac {5}{3}}-3 x^{\frac {8}{3}}+16 A \,x^{\frac {4}{3}}+16 B =0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=-\frac {-16 y x^{\frac {5}{3}}+3 x^{\frac {8}{3}}-16 A \,x^{\frac {4}{3}}-16 B}{16 y x^{\frac {5}{3}}} \end {array} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-y(x)=-3/16*x+A*x^(-1/3)+B*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]==-3/16*x+A*x^(-1/3)+B*x^(-5/3),y[x],x,IncludeSingularSolutions -> True]
Not solved