60.1.113 problem 113

Internal problem ID [10127]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 113
Date solved : Monday, January 27, 2025 at 06:28:43 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

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

\[ \frac {x^{a} y+x^{a} \sqrt {x^{2}+y^{2}}-c_{1} x}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.231 (sec). Leaf size: 16

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

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