73.8.34 problem 13.5 (j)

Internal problem ID [15171]
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 : Monday, March 31, 2025 at 01:29:58 PM
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*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x) = diff(y(x),x)*(diff(y(x),x)-2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (2\right )-\ln \left (c_1 \,{\mathrm e}^{-2 x}-2 c_2 \right ) \]

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

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

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

✓ Sympy. Time used: 0.996 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(Derivative(y(x), x) - 2)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + 2 x - \log {\left (C_{2} + e^{2 x} \right )} \]