82.23.4 problem Ex. 4

Internal problem ID [18860]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:31:07 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.386 (sec). Leaf size: 35

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

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