Internal problem ID [10387]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 1, section 1.2. Riccati Equation. 1.2.2. Equations Containing Power
Functions
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {2 y^{\prime } x^{2}-2 y^{2}-y x=-2 a^{2} x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(2*x^2*diff(y(x),x)=2*y(x)^2+x*y(x)-2*a^2*x,y(x), singsol=all)
\[ y \left (x \right ) = -i \tan \left (\frac {2 i a -c_{1} \sqrt {x}}{\sqrt {x}}\right ) a \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.619 (sec). Leaf size: 43
DSolve[2*x^2*y'[x]==2*y[x]^2+x*y[x]-2*a^2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sqrt {-a^2} \sqrt {x} \tan \left (\frac {2 \sqrt {-a^2}}{\sqrt {x}}-c_1\right ) \]