73.8.34 problem 13.5 (j)

Internal problem ID [15242]
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)
Date solved : Tuesday, January 28, 2025 at 07:50:42 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }-2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.823 (sec). Leaf size: 41

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

\[ y(x)\to \int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-2) K[1]}dK[1]\&\right ][c_1+K[2]]dK[2]+c_2 \]