76.5.5 problem 5

Internal problem ID [17425]
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 : 5
Date solved : Tuesday, January 28, 2025 at 10:07:12 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

\[ -\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )+\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 18

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

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