83.23.4 problem 4

Internal problem ID [19285]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:24:26 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 25

DSolve[y[x]==x*D[y[x],x]-D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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