Internal problem ID [13494]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.217 (sec). Leaf size: 15
DSolve[y''[x]==y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\log (x+c_1) \]