75.5.3 problem 102

Internal problem ID [16668]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 102
Date solved : Monday, March 31, 2025 at 03:04:28 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 12

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

\[ y = x \,{\mathrm e}^{c_1 x +1} \]

✓ Mathematica. Time used: 0.238 (sec). Leaf size: 24

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

\begin{align*} y(x)\to x e^{1+e^{c_1} x} \\ y(x)\to e x \\ \end{align*}

✓ Sympy. Time used: 0.793 (sec). Leaf size: 10

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

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