Internal problem ID [12099]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{2}-y^{\prime }-x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve(diff(y(x),x)^2-diff(y(x),x)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{4} x^{2}+\frac {1}{2} x +\frac {1}{4} y \left (x \right ) = -c_{1}^{2}+c_{1} x +c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 28
DSolve[(y'[x])^2-y'[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+1-c_1) y(x)\to \frac {1}{4} (x+1)^2 \end{align*}