Internal problem ID [3175]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 429.
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: 18
dsolve(y(x)*diff(y(x),x) = sqrt(y(x)^2+a^2),y(x), singsol=all)
\[ x -\sqrt {y \relax (x )^{2}+a^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 61
DSolve[y[x] y'[x]==Sqrt[a^2+y[x]^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 -i a \\ y(x)\to i a \\ \end{align*}