Internal problem ID [2568]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime } x -\sqrt {y^{2}-9}=0} \end {gather*} With initial conditions \begin {align*} [y \left ({\mathrm e}^{4}\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 12
dsolve([x*y(x)*diff(y(x),x)=sqrt(y(x)^2-9),y(exp(4)) = 5],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {9+\ln \relax (x )^{2}} \]
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 32
DSolve[{x*y[x]*y'[x]==Sqrt[y[x]^2-9],y[Exp[4]]==5},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {\log ^2(x)+9} \\ y(x)\to \sqrt {(\log (x)-16) \log (x)+73} \\ \end{align*}