Internal problem ID [10801]
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 1.3.3-2. Equations
of the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-\frac {a \left (\frac {\left (n +4\right ) x}{2+n}-2\right ) x^{-\frac {2 n +1}{n}} y}{n}=\frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (2+n \right )\right ) x^{-\frac {2+3 n}{n}}}{n \left (2+n \right )}} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-a/n*((n+4)/(n+2)*x-2)*x^(-(2*n+1)/n)*y(x)=a^2/(n*(n+2))*(2*x^2+(n^2+n-4)*x-(n-1)*(n+2))*x^(-(3*n+2)/n),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-a/n*((n+4)/(n+2)*x-2)*x^(-(2*n+1)/n)*y[x]==a^2/(n*(n+2))*(2*x^2+(n^2+n-4)*x-(n-1)*(n+2))*x^(-(3*n+2)/n),y[x],x,IncludeSingularSolutions -> True]
Not solved