Internal problem ID [10008]
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: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-\left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (x a +b \right )^{-\lambda -2} y+\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (x a +b \right )^{-2 \lambda -3}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)=(a*(n-1)*x+b*(2*lambda+n))*x^(lambda-1)*(a*x+b)^(-lambda-2)*y(x)-(a*n*x+b*(lambda+n))*x^(2*lambda-1)*(a*x+b)^(-2*lambda-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]==(a*(n-1)*x+b*(2*\[Lambda]+n))*x^(\[Lambda]-1)*(a*x+b)^(-\[Lambda]-2)*y[x]-(a*n*x+b*(\[Lambda]+n))*x^(2*\[Lambda]-1)*(a*x+b)^(-2*\[Lambda]-3),y[x],x,IncludeSingularSolutions -> True]
Not solved