Internal problem ID [7604]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+a y^{2}-b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x) + a*y(x)^2 - b=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tanh \left (c_{1} \sqrt {a b}+x \sqrt {a b}\right ) \sqrt {a b}}{a} \]
✓ Solution by Mathematica
Time used: 4.101 (sec). Leaf size: 63
DSolve[y'[x] + a*y[x]^2 - b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {b} \tanh \left (\sqrt {a} \sqrt {b} (x+c_1)\right )}{\sqrt {a}} \\ y(x)\to -\frac {\sqrt {b}}{\sqrt {a}} \\ y(x)\to \frac {\sqrt {b}}{\sqrt {a}} \\ \end{align*}