29.37.9 problem 1125

Internal problem ID [5667]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1125
Date solved : Monday, January 27, 2025 at 01:02:32 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.373 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 27

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

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