Internal problem ID [3436]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 180.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x y^{\prime }+a \,x^{2} y^{2}+2 y=b} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 104
dsolve(x*diff(y(x),x)+a*x^2*y(x)^2+2*y(x) = b,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {-a b}\, c_{1} \operatorname {BesselY}\left (1, \sqrt {-a b}\, x \right )}{a x \left (c_{1} \operatorname {BesselY}\left (0, \sqrt {-a b}\, x \right )+\operatorname {BesselJ}\left (0, \sqrt {-a b}\, x \right )\right )}-\frac {\operatorname {BesselJ}\left (1, \sqrt {-a b}\, x \right ) \sqrt {-a b}}{a x \left (c_{1} \operatorname {BesselY}\left (0, \sqrt {-a b}\, x \right )+\operatorname {BesselJ}\left (0, \sqrt {-a b}\, x \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 158
DSolve[x y'[x]+a x^2 y[x]^2+2 y[x]==b,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \sqrt {b} \left (\operatorname {BesselY}\left (1,-i \sqrt {a} \sqrt {b} x\right )-c_1 \operatorname {BesselJ}\left (1,i \sqrt {a} \sqrt {b} x\right )\right )}{\sqrt {a} x \left (\operatorname {BesselY}\left (0,-i \sqrt {a} \sqrt {b} x\right )+c_1 \operatorname {BesselJ}\left (0,i \sqrt {a} \sqrt {b} x\right )\right )} y(x)\to -\frac {i \sqrt {b} \operatorname {BesselJ}\left (1,i \sqrt {a} \sqrt {b} x\right )}{\sqrt {a} x \operatorname {BesselJ}\left (0,i \sqrt {a} \sqrt {b} x\right )} \end{align*}