Internal problem ID [3256]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 512.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime } x -a -b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(x*y(x)*diff(y(x),x) = a+b*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {b \left (x^{2 b} c_{1} b -a \right )}}{b} \\ y \relax (x ) = -\frac {\sqrt {b \left (x^{2 b} c_{1} b -a \right )}}{b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.249 (sec). Leaf size: 94
DSolve[x y[x] y'[x]==a+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-a+e^{2 b (\log (x)+c_1)}}}{\sqrt {b}} \\ y(x)\to \frac {\sqrt {-a+e^{2 b (\log (x)+c_1)}}}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}