53.4.22 problem 24

Internal problem ID [8510]
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
Date solved : Monday, January 27, 2025 at 04:08:38 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=diff(y(x),x)^2,y(x), singsol=all)
 

\[ y = -\ln \left (-c_{1} x -c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 15

DSolve[D[y[x],{x,2}]==(D[y[x],x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2-\log (x+c_1) \]