Internal problem ID [9747]
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]
\[ \boxed {y^{\prime } x -a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}+b=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x*diff(y(x),x)=a*x^n*(y(x)+b*ln(x))^2-b,y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (x \right ) b +\frac {1}{c_{1} -\frac {a \,x^{n}}{n}} \]
✓ Solution by Mathematica
Time used: 0.425 (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*}