82.19.2 problem Ex. 2

Internal problem ID [18849]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 43
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:28:57 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: 0.017 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 23

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*}