81.7.5 problem 6

Internal problem ID [18623]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 6
Date solved : Thursday, March 13, 2025 at 12:26:44 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 14

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= {\mathrm e}^{c_{1} x} c_{2} \\ \end{align*}

✓ Mathematica. Time used: 0.113 (sec). Leaf size: 14

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

\[ y(x)\to c_2 e^{c_1 x} \]

✗ Sympy

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

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