29.7.20 problem 195

Internal problem ID [4795]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 195
Date solved : Monday, January 27, 2025 at 09:38:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.260 (sec). Leaf size: 18

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

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