Internal problem ID [13186]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.5 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-y^{\prime } \left (y^{\prime }-2\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)=diff(y(x),x)*(diff(y(x),x)-2),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\frac {{\mathrm e}^{-2 x} c_{1}}{2}-c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 60.076 (sec). Leaf size: 23
DSolve[y''[x]==y'[x]*(y'[x]-2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-2 \text {arctanh}\left (1+2 e^{2 (x+c_1)}\right ) \]