75.9.8 problem 227

Internal problem ID [16845]
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 : 227
Date solved : Tuesday, January 28, 2025 at 09:34:41 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} {y^{\prime }}^{2} x -y^{\prime } y-y^{\prime }+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.159 (sec). Leaf size: 38

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

\begin{align*} y &= -2 \sqrt {x}-1 \\ y &= 2 \sqrt {x}-1 \\ y &= \frac {c_{1}^{2} x -c_{1} +1}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 46

DSolve[x*D[y[x],x]^2-y[x]*D[y[x],x]-D[y[x],x]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x-1+\frac {1}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {x}-1 \\ y(x)\to 2 \sqrt {x}-1 \\ \end{align*}