Internal problem ID [3845]
Book: Differential and integral calculus, vol II By N. Piskunov. 1974
Section: Chapter 1
Problem number: example page 47.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_Clairaut]
Solve \begin {gather*} \boxed {y-y^{\prime } x -\frac {a y^{\prime }}{\sqrt {\left (y^{\prime }\right )^{2}+1}}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)=x*diff(y(x),x)+ a*diff(y(x),x)/(sqrt(1+diff(y(x),x)^2)),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 33.008 (sec). Leaf size: 27
DSolve[y[x]==x*y'[x]+ a*y'[x]/(Sqrt[1+(y'[x])^2]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {a}{\sqrt {1+c_1{}^2}}\right ) \\ y(x)\to 0 \\ \end{align*}