75.9.7 problem 226

Internal problem ID [16844]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number : 226
Date solved : Tuesday, January 28, 2025 at 09:34:41 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 17

dsolve(y(x)=x*diff(y(x),x)+diff(y(x),x)^2,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: 0.006 (sec). Leaf size: 23

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*}