29.7.19 problem 194

Internal problem ID [4794]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 194
Date solved : Monday, January 27, 2025 at 09:38:17 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: 0.029 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.310 (sec). Leaf size: 13

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

\[ y(x)\to x \sinh (\log (x)+c_1) \]