Internal problem ID [3423]
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]
\[ \boxed {x y^{\prime }-y-b y^{2}=x^{2} a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x*diff(y(x),x) = a*x^2+y(x)+b*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\tan \left (c_{1} \sqrt {a b}+x \sqrt {a b}\right ) x \sqrt {a b}}{b} \]
✓ Solution by Mathematica
Time used: 17.546 (sec). Leaf size: 33
DSolve[x y'[x]==a x^2+y[x]+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {a} x \tan \left (\sqrt {a} \sqrt {b} (x+c_1)\right )}{\sqrt {b}} \]