60.1.114 problem 114

Internal problem ID [10128]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 114
Date solved : Tuesday, January 28, 2025 at 04:25:47 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.785 (sec). Leaf size: 28

dsolve(x*diff(y(x),x) - x*sqrt(y(x)^2 + x^2) - y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 12

DSolve[x*D[y[x],x] - x*Sqrt[y[x]^2 + x^2] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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