Internal problem ID [7789]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 209.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime } y-\sqrt {a y^{2}+b}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(y(x)*diff(y(x),x)-sqrt(a*y(x)^2+b)=0,y(x), singsol=all)
\[ x -\frac {\sqrt {a y \relax (x )^{2}+b}}{a}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.442 (sec). Leaf size: 94
DSolve[y[x]*y'[x]-Sqrt[a*y[x]^2+b]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-b+a^2 (x+c_1){}^2}}{\sqrt {a}} \\ y(x)\to \frac {\sqrt {-b+a^2 (x+c_1){}^2}}{\sqrt {a}} \\ y(x)\to -\frac {i \sqrt {b}}{\sqrt {a}} \\ y(x)\to \frac {i \sqrt {b}}{\sqrt {a}} \\ \end{align*}