Internal problem ID [5142]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page
218
Problem number: Problem 3.34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x y^{\prime }-y-x \sqrt {x^{2}-y^{2}}\, y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve(x*diff(y(x),x)-y(x)=x*sqrt(x^2-y(x)^2)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x )-\arctan \left (\frac {y \relax (x )}{\sqrt {x^{2}-y \relax (x )^{2}}}\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.86 (sec). Leaf size: 29
DSolve[x*y'[x]-y[x]==x*Sqrt[x^2-y[x]^2]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]