40.5.7 problem 23

Internal problem ID [6672]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page 65
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:18:54 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: 0.016 (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: 0.010 (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*}