75.11.15 problem 274

Internal problem ID [16866]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 274
Date solved : Tuesday, January 28, 2025 at 09:35:50 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.809 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 37

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