15.2.5 problem 5

Internal problem ID [2875]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:21:36 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 27

dsolve(x*diff(y(x),x)-y(x)=sqrt(x^2-y(x)^2),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: 0.265 (sec). Leaf size: 18

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

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