Internal problem ID [2915]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 167.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -a \,x^{2}-y-b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(x*diff(y(x),x) = a*x^2+y(x)+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (c_{1} \sqrt {a b}+x \sqrt {a b}\right ) x \sqrt {a b}}{b} \]
✓ Solution by Mathematica
Time used: 12.07 (sec). Leaf size: 33
DSolve[x y'[x]==a x^2+y[x]+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {a} x \tan \left (\sqrt {a} \sqrt {b} (x+c_1)\right )}{\sqrt {b}} \\ \end{align*}