Internal problem ID [9749]
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: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -\left (a y+\ln \relax (x ) b \right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(x*diff(y(x),x)=(a*y(x)+b*ln(x))^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \relax (x ) a b -\tan \left (c_{1} a \sqrt {b a}+\ln \relax (x ) \sqrt {b a}\right ) \sqrt {b a}}{a^{2}} \]
✓ Solution by Mathematica
Time used: 3.515 (sec). Leaf size: 43
DSolve[x*y'[x]==(a*y[x]+b*Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {b \log (x)}{a}+\sqrt {\frac {b}{a^3}} \tan \left (a^2 \sqrt {\frac {b}{a^3}} \log (x)+c_1\right ) \\ \end{align*}