60.1.91 problem 93

Internal problem ID [10105]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 93
Date solved : Sunday, March 30, 2025 at 03:16:12 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=x*diff(y(x),x)-y(x)-x*cos(ln(ln(x)))/ln(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\sin \left (\ln \left (\ln \left (x \right )\right )\right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 32

ode=x*D[y[x],x] - y[x] - x*Cos[Log[Log[x]]]/Log[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \left (\int _1^x\frac {\cos (\log (\log (K[1])))}{K[1] \log (K[1])}dK[1]+c_1\right ) \]

✓ Sympy. Time used: 2.136 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = x \left (C_{1} + \sin {\left (\log {\left (\log {\left (x \right )} \right )} \right )}\right ) \]