Internal problem ID [6049]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 99. Clairaut’s equation. EXERCISES Page
320
Problem number: 10.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-2 y y^{\prime }+4 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.197 (sec). Leaf size: 29
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+4*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -2 x \\ y \relax (x ) = 2 x \\ y \relax (x ) = -\frac {\left (-\frac {x^{2}}{c_{1}^{2}}-4\right ) c_{1}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.353 (sec). Leaf size: 43
DSolve[x*(y'[x])^2-2*y[x]*y'[x]+4*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x \cosh (-\log (x)+c_1) \\ y(x)\to -2 x \cosh (\log (x)+c_1) \\ y(x)\to -2 x \\ y(x)\to 2 x \\ \end{align*}