Internal problem ID [9734]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -a y^{2}-\ln \relax (x ) b -c=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 138
dsolve(x*diff(y(x),x)=a*y(x)^2+b*ln(x)+c,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (b a \right )^{\frac {1}{3}} c_{1} \AiryBi \left (1, -\frac {\left (b a \right )^{\frac {1}{3}} \left (b \ln \relax (x )+c \right )}{b}\right )}{a \left (c_{1} \AiryBi \left (-\frac {\left (b a \right )^{\frac {1}{3}} \left (b \ln \relax (x )+c \right )}{b}\right )+\AiryAi \left (-\frac {\left (b a \right )^{\frac {1}{3}} \left (b \ln \relax (x )+c \right )}{b}\right )\right )}+\frac {\left (b a \right )^{\frac {1}{3}} \AiryAi \left (1, -\frac {\left (b a \right )^{\frac {1}{3}} \left (b \ln \relax (x )+c \right )}{b}\right )}{a \left (c_{1} \AiryBi \left (-\frac {\left (b a \right )^{\frac {1}{3}} \left (b \ln \relax (x )+c \right )}{b}\right )+\AiryAi \left (-\frac {\left (b a \right )^{\frac {1}{3}} \left (b \ln \relax (x )+c \right )}{b}\right )\right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*y'[x]==a*y[x]^2+b*Log[x]+c,y[x],x,IncludeSingularSolutions -> True]
Not solved