Internal problem ID [8545]
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]
\[ \boxed {y y^{\prime }-\sqrt {a y^{2}+b}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(y(x)*diff(y(x),x)-sqrt(a*y(x)^2+b)=0,y(x), singsol=all)
\[ \frac {-\sqrt {a y \left (x \right )^{2}+b}+\left (x +c_{1} \right ) a}{a} = 0 \]
✓ Solution by Mathematica
Time used: 0.531 (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*}