Internal problem ID [10492]
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]
\[ \boxed {y^{\prime } x -\left (a y+b \ln \left (x \right )\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(x*diff(y(x),x)=(a*y(x)+b*ln(x))^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\ln \left (x \right ) a b +\tan \left (\left (\ln \left (x \right )+c_{1} \right ) \sqrt {a b}\right ) \sqrt {a b}}{a^{2}} \]
✓ Solution by Mathematica
Time used: 6.524 (sec). Leaf size: 43
DSolve[x*y'[x]==(a*y[x]+b*Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {b \log (x)}{a}+\sqrt {\frac {b}{a^3}} \tan \left (a^2 \sqrt {\frac {b}{a^3}} \log (x)+c_1\right ) \]