Internal problem ID [9751]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.5-2
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }-a \,x^{n} \left (y+b \ln \relax (x )\right )^{2}+b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 23
dsolve(x*diff(y(x),x)=a*x^n*(y(x)+b*ln(x))^2-b,y(x), singsol=all)
\[ y \relax (x ) = -b \ln \relax (x )+\frac {1}{c_{1}-\frac {x^{n} a}{n}} \]
✓ Solution by Mathematica
Time used: 0.437 (sec). Leaf size: 35
DSolve[x*y'[x]==a*x^n*(y[x]+b*Log[x])^2-b,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -b \log (x)+\frac {n}{-a x^n+c_1 n} \\ y(x)\to -b \log (x) \\ \end{align*}