82.19.1 problem Ex. 1

Internal problem ID [18848]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 43
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:28:51 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.190 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 27

DSolve[y[x]==x*D[y[x],x]+a*Sqrt[1+D[y[x],x]^2],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*}