Internal problem ID [3145]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 399.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {x^{\frac {3}{2}} y^{\prime }-a -b \,x^{\frac {3}{2}} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 119
dsolve(x^(3/2)*diff(y(x),x) = a+b*x^(3/2)*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 a \left (\BesselJ \left (1, 4 \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}\right ) c_{1}+\BesselY \left (1, 4 \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}\right )\right )}{\sqrt {x}\, \left (-2 \BesselJ \left (0, 4 \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}\right ) \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}} c_{1}-2 \BesselY \left (0, 4 \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}\right ) \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}+\BesselJ \left (1, 4 \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}\right ) c_{1}+\BesselY \left (1, 4 \sqrt {b}\, \sqrt {a}\, x^{\frac {1}{4}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 73
DSolve[x^(3/2) y'[x]==a+ b x^(3/2) y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\, _0\tilde {F}_1\left (;2;-4 a b \sqrt {x}\right )}{b x \, _0F_1\left (;3;-4 a b \sqrt {x}\right )} \\ y(x)\to -\frac {\, _0\tilde {F}_1\left (;2;-4 a b \sqrt {x}\right )}{b x \, _0F_1\left (;3;-4 a b \sqrt {x}\right )} \\ \end{align*}