76.1.26 problem 26

Internal problem ID [17325]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 10:00:20 AM
CAS classification : [_separable]

\begin{align*} 2 y^{\prime } y&=\frac {x}{\sqrt {x^{2}-4}} \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.269 (sec). Leaf size: 43

dsolve([2*y(x)*diff(y(x),x)=x/sqrt(x^2-4),y(3) = -1],y(x), singsol=all)
 

\[ y = -\frac {\sqrt {\sqrt {x^{2}-4}\, \left (\left (-\sqrt {5}+1\right ) \sqrt {x^{2}-4}+x^{2}-4\right )}}{\sqrt {x^{2}-4}} \]

✓ Solution by Mathematica

Time used: 1.734 (sec). Leaf size: 29

DSolve[{2*y[x]*D[y[x],x]==x/Sqrt[x^2-4],{y[3]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {\sqrt {x^2-4}-\sqrt {5}+1} \]