15.2.7 problem 7

Internal problem ID [2877]
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 : 7
Date solved : Monday, January 27, 2025 at 06:22:34 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }-y+\sqrt {y^{2}-x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(x*diff(y(x),x)-y(x)+sqrt(y(x)^2-x^2)=0,y(x), singsol=all)
 

\[ y+\sqrt {y^{2}-x^{2}}-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 16

DSolve[x*D[y[x],x]-y[x]+Sqrt[y[x]^2-x^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

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