85.33.65 problem 66

Internal problem ID [22688]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 66
Date solved : Thursday, October 02, 2025 at 09:06:38 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 10

ode:=x*diff(y(x),x)+y(x)*ln(x) = y(x)*ln(y(x))+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \,{\mathrm e}^{c_1 x} \]

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to x e^{e^{c_1} x}\\ y(x)&\to x \end{align*}

✓ Sympy. Time used: 0.344 (sec). Leaf size: 8

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

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