81.2.1 problem 1

Internal problem ID [18538]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 1
Date solved : Monday, March 31, 2025 at 05:41:43 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }-2 y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)-2*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\frac {c_2 +x}{c_1}\right )}{c_1} \]

✓ Mathematica. Time used: 9.662 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-2*y[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {c_1} \tan \left (\sqrt {c_1} (x+c_2)\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - Derivative(y(x), (x, 2))/(2*y(x)) cannot be solved by the factorable group method