Internal problem ID [2174]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 28.
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 {4 x^{2}-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 29
dsolve(x*diff(y(x),x)-y(x)=sqrt(4*x^2-y(x)^2),y(x), singsol=all)
\[ -\arctan \left (\frac {y \relax (x )}{\sqrt {4 x^{2}-y \relax (x )^{2}}}\right )+\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.414 (sec). Leaf size: 18
DSolve[x*y'[x]-y[x]==Sqrt[4*x^2-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x \cosh (i \log (x)+c_1) \\ \end{align*}