9.2 problem Ex 2

Internal problem ID [10143]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [y=_G(x,y')]

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

Solution by Maple

Time used: 0.094 (sec). Leaf size: 27

dsolve((x*diff(y(x),x)-y(x))/sqrt(x^2-y(x)^2)=x*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: 0.55 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\text {ArcTan}\left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]