Internal problem ID [11824]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 47.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-{y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.375 (sec). Leaf size: 17
dsolve([y(x)=x*diff(y(x),x)+diff(y(x),x)^2,y(2) = -1],y(x), singsol=all)
\begin{align*} y \left (x \right ) = 1-x y \left (x \right ) = -\frac {x^{2}}{4} \end{align*}
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 21
DSolve[{y[x]==x*y'[x]+y'[x]^2,{y[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1-x y(x)\to -\frac {x^2}{4} \end{align*}