60.1.552 problem 555

Internal problem ID [10566]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 555
Date solved : Monday, January 27, 2025 at 09:05:46 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.365 (sec). Leaf size: 15

dsolve((diff(y(x),x)^2+1)^(1/2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {c_{1}^{2}+1}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 25

DSolve[-y[x] + x*D[y[x],x] + Sqrt[1 + D[y[x],x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x+\sqrt {1+c_1{}^2} \\ y(x)\to 1 \\ \end{align*}