Internal problem ID [6089]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=diff(y(x),x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (-c_{1} x -c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.298 (sec). Leaf size: 15
DSolve[y''[x]==(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\log (x+c_1) \\ \end{align*}