Internal problem ID [3176]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 430.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y y^{\prime }-\sqrt {y^{2}-a^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(y(x)*diff(y(x),x) = sqrt(y(x)^2-a^2),y(x), singsol=all)
\[ x +\frac {\left (a -y \relax (x )\right ) \left (y \relax (x )+a \right )}{\sqrt {y \relax (x )^{2}-a^{2}}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 51
DSolve[y[x] y'[x]==Sqrt[y[x]^2-a^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {a^2+(x+c_1){}^2} \\ y(x)\to \sqrt {a^2+(x+c_1){}^2} \\ y(x)\to -a \\ y(x)\to a \\ \end{align*}