53.3.4 problem 6

Internal problem ID [8466]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 99. Clairaut equation. EXERCISES Page 320
Problem number : 6
Date solved : Monday, January 27, 2025 at 04:06:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 19

dsolve(diff(y(x),x)^2-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x^{2}}{4} \\ y &= c_{1} \left (x -c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[(D[y[x],x])^2-x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x-c_1) \\ y(x)\to \frac {x^2}{4} \\ \end{align*}