76.5.8 problem 8

Internal problem ID [17428]
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 2.7 (Substitution Methods). Problems at page 108
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 10:08:16 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(x*diff(y(x),x)-4*sqrt( y(x)^2-x^2)=y(x),y(x), singsol=all)
 

\[ \frac {-c_{1} x^{5}+\sqrt {y^{2}-x^{2}}+y}{x^{5}} = 0 \]

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 16

DSolve[x*D[y[x],x]-4*Sqrt[ y[x]^2-x^2]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \cosh (4 \log (x)+c_1) \]