31.6.13 problem 13

Internal problem ID [5762]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 13
Date solved : Monday, January 27, 2025 at 01:13:00 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.527 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.350 (sec). Leaf size: 38

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

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