Internal problem ID [5338]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page
74
Problem number: 10.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } x +2 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(y(x)=diff(y(x),x)*x-2*diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y = \frac {x^{2}}{8} y = -2 c_{1}^{2}+c_{1} x \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[y[x]==y'[x]*x-2*y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-2 c_1) y(x)\to \frac {x^2}{8} \end{align*}