Internal problem ID [9741]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.5-1. Equations Containing
Logarithmic Functions
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {x^{2} \ln \left (x a \right ) \left (y^{\prime }-y^{2}\right )-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(x^2*ln(a*x)*(diff(y(x),x)-y(x)^2)=1,y(x), singsol=all)
\[ y \relax (x ) = -\frac {c_{1} \expIntegral \left (1, -\ln \left (a x \right )\right )-1}{x \left (\left (c_{1} \expIntegral \left (1, -\ln \left (a x \right )\right )-1\right ) \ln \left (a x \right )+c_{1} a x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^2*Log[a*x]*(y'[x]-y[x]^2)==1,y[x],x,IncludeSingularSolutions -> True]
Not solved