Internal problem ID [10007]
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: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-\left (a \left (2 n +1\right ) x^{2}+x c +b \left (2 n -1\right )\right ) x^{n -2} y+\left (n \,a^{2} x^{4}+a c \,x^{3}+b^{2} n +b c x +d \,x^{2}\right ) x^{2 n -3}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)=(a*(2*n+1)*x^2+c*x+b*(2*n-1))*x^(n-2)*y(x)-(n*a^2*x^4+a*c*x^3+d*x^2+b*c*x+n*b^2)*x^(2*n-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*(2*n+1)*x^2+c*x+b*(2*n-1))*x^(n-2)*y[x]-(n*a^2*x^4+a*c*x^3+d*x^2+b*c*x+n*b^2)*x^(2*n-3),y[x],x,IncludeSingularSolutions -> True]
Timed out