Internal problem ID [3844]
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]
\[ \boxed {y-y^{\prime } x -\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}=0} \]
✓ Solution by Maple
Time used: 1.5 (sec). Leaf size: 18
dsolve(y(x)=x*diff(y(x),x)+ a*diff(y(x),x)/(sqrt(1+diff(y(x),x)^2)),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +\frac {a c_{1}}{\sqrt {c_{1}^{2}+1}} \]
✓ Solution by Mathematica
Time used: 35.248 (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*}