75.9.10 problem 229

Internal problem ID [16847]
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 : 229
Date solved : Tuesday, January 28, 2025 at 09:34:48 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 33

dsolve(x=y(x)/diff(y(x),x)+1/diff(y(x),x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 47

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

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