73.17.16 problem 16

Internal problem ID [15550]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 08:01:50 AM
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: 0.028 (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: 0.196 (sec). Leaf size: 15

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

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