25.1.26 problem 26

Internal problem ID [4238]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 26
Date solved : Monday, January 27, 2025 at 08:43:31 AM
CAS classification : [_separable]

\begin{align*} x y y^{\prime }&=\sqrt {y^{2}-9} \end{align*}

With initial conditions

\begin{align*} y \left ({\mathrm e}^{4}\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.076 (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)
 

\[ y \left (x \right ) = \sqrt {9+\ln \left (x \right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 33

DSolve[{x*y[x]*D[y[x],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 ^2(x)-16 \log (x)+73} \\ \end{align*}