29.37.8 problem 1123

Internal problem ID [5666]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1123
Date solved : Monday, January 27, 2025 at 01:02:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.536 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.365 (sec). Leaf size: 37

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

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