7.3.21 problem 21

Internal problem ID [61]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 21
Date solved : Friday, February 07, 2025 at 07:47:24 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: 0.078 (sec). Leaf size: 34

dsolve([2*y(x)*diff(y(x),x)= x/sqrt(x^2-16),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: 1.736 (sec). Leaf size: 20

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

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