Internal problem ID [2809]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 54.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-a -b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x) = a+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (c_{1} \sqrt {a b}+x \sqrt {a b}\right ) \sqrt {a b}}{b} \]
✓ Solution by Mathematica
Time used: 7.57 (sec). Leaf size: 68
DSolve[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} (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*}