40.6.1 problem 10

Internal problem ID [6681]
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
Date solved : Monday, January 27, 2025 at 02:20:57 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }-2 {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 19

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 &= c_1 \left (-2 c_1 +x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 25

DSolve[y[x]==D[y[x],x]*x-2*D[y[x],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*}