2.5 problem 5

Internal problem ID [1904]

Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 5.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]

Solve \begin {gather*} \boxed {y^{\prime } x -y-\sqrt {x^{2}-y^{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

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

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

Solution by Mathematica

Time used: 0.436 (sec). Leaf size: 17

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

\begin{align*} y(x)\to x \cosh (i \log (x)+c_1) \\ \end{align*}