62.12.9 problem Ex 10

Internal problem ID [12855]
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 19. Summary. Page 29
Problem number : Ex 10
Date solved : Tuesday, January 28, 2025 at 04:27:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 18

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

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