29.25.32 problem 729

Internal problem ID [5319]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 729
Date solved : Monday, January 27, 2025 at 11:10:44 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.490 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}