Internal problem ID [2914]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 166.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -a -b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 30
dsolve(x*diff(y(x),x) = a+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\ln \relax (x ) \sqrt {a b}+c_{1} \sqrt {a b}\right ) \sqrt {a b}}{b} \]
✓ Solution by Mathematica
Time used: 6.784 (sec). Leaf size: 69
DSolve[x y'[x]==a+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {a} \tan \left (\sqrt {a} \sqrt {b} (\log (x)+c_1)\right )}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}