8.3.20 problem 21

Internal problem ID [696]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:58:15 AM
CAS classification : [_separable]

\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \end{align*}

With initial conditions

\begin{align*} y \left (5\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 34

dsolve([2*y(x)*diff(y(x),x) = x/(x^2-16)^(1/2),y(5) = 2],y(x), singsol=all)
 

\[ y = \frac {\sqrt {\sqrt {x^{2}-16}\, \left (x^{2}+\sqrt {x^{2}-16}-16\right )}}{\sqrt {x^{2}-16}} \]

✓ Solution by Mathematica

Time used: 1.718 (sec). Leaf size: 20

DSolve[{2*y[x]*D[y[x],x] == x/(x^2-16)^(1/2),y[5]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {\sqrt {x^2-16}+1} \]