82.44.3 problem Ex. 3

Internal problem ID [18888]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 99
Problem number : Ex. 3
Date solved : Thursday, March 13, 2025 at 01:08:12 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.958 (sec). Leaf size: 63

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

\begin{align*} y(x)\to e^{\frac {1}{2} \left (e^{x+c_2}-c_1 e^{-x-c_2}\right )} \\ y(x)\to e^{\frac {1}{2} \left (e^{-x-c_2}-c_1 e^{x+c_2}\right )} \\ \end{align*}

✗ Sympy

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

TypeError : cannot determine truth value of Relational