Internal problem ID [2928]
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]
Solve \begin {gather*} \boxed {y^{\prime } x +a \,x^{2} y^{2}+2 y-b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 104
dsolve(x*diff(y(x),x)+a*x^2*y(x)^2+2*y(x) = b,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\sqrt {-a b}\, c_{1} \BesselY \left (1, \sqrt {-a b}\, x \right )}{a x \left (c_{1} \BesselY \left (0, \sqrt {-a b}\, x \right )+\BesselJ \left (0, \sqrt {-a b}\, x \right )\right )}-\frac {\BesselJ \left (1, \sqrt {-a b}\, x \right ) \sqrt {-a b}}{a x \left (c_{1} \BesselY \left (0, \sqrt {-a b}\, x \right )+\BesselJ \left (0, \sqrt {-a b}\, x \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.236 (sec). Leaf size: 125
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 {\sqrt {b} \left (i Y_1\left (-i \sqrt {a} \sqrt {b} x\right )+c_1 I_1\left (\sqrt {a} \sqrt {b} x\right )\right )}{\sqrt {a} x \left (c_1 \, _0\tilde {F}_1\left (;1;\frac {1}{4} a b x^2\right )+Y_0\left (-i \sqrt {a} \sqrt {b} x\right )\right )} \\ y(x)\to \frac {b \, _0\tilde {F}_1\left (;2;\frac {1}{4} a b x^2\right )}{2 \, _0\tilde {F}_1\left (;1;\frac {1}{4} a b x^2\right )} \\ \end{align*}