56.1.17 problem 17

Internal problem ID [8729]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 17
Date solved : Monday, January 27, 2025 at 04:20:52 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} \frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 18

dsolve((1/4)*diff(y(x),x)^2-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 25

DSolve[(1/4)*(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-\frac {c_1{}^2}{4} \\ y(x)\to x^2 \\ \end{align*}