Internal problem ID [3434]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 178.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {x y^{\prime }+\left (2+a x y\right ) y=-b x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(x*diff(y(x),x)+b*x+(2+a*x*y(x))*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {-\frac {i \sqrt {a}\, \sqrt {b}\, x -1}{x}+\frac {{\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x}}{c_{1} -\frac {i {\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x}}{2 \sqrt {a}\, \sqrt {b}}}}{a} \]
✓ Solution by Mathematica
Time used: 3.304 (sec). Leaf size: 43
DSolve[x y'[x]+b x+(2+a x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{a x}-\sqrt {\frac {b}{a}} \tan \left (a x \sqrt {\frac {b}{a}}-c_1\right ) \]