69.1.67 problem 95

Internal problem ID [14220]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 95
Date solved : Tuesday, January 28, 2025 at 06:22:27 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.501 (sec). Leaf size: 17

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

\[ y = c_{1} x +\sqrt {-c_{1}^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 27

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

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