Internal problem ID [6104]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 40.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (y^{\prime \prime }\right )^{2}-x y^{\prime \prime }+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.625 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)^2-x*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{3}}{12}+c_{1} \\ y \relax (x ) = \frac {1}{2} c_{1} x^{2}-c_{1}^{2} x +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 21
DSolve[(y''[x])^2-x*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} c_1 x (x-2 c_1)+c_2 \\ \end{align*}