77.48.16 problem Ex 16 page 111

Internal problem ID [20892]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 16 page 111
Date solved : Thursday, October 02, 2025 at 06:46:12 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.037 (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);
 

\[ y = {\mathrm e}^{-\frac {c_1 \,{\mathrm e}^{x}}{2}+\frac {c_2 \,{\mathrm e}^{-x}}{2}} \]

✓ Mathematica. Time used: 0.92 (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: _X0**2 < 2