10.3.6 problem 6

Internal problem ID [1171]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 6
Date solved : Saturday, March 29, 2025 at 10:44:22 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

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

\[ y = \left (\int \frac {\cot \left (t \right ) {\mathrm e}^{-\operatorname {Ei}_{1}\left (-\ln \left (t \right )\right )}}{\ln \left (t \right )}d t +c_1 \right ) {\mathrm e}^{\operatorname {Ei}_{1}\left (-\ln \left (t \right )\right )} \]

✓ Mathematica. Time used: 0.123 (sec). Leaf size: 36

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

\[ y(t)\to e^{-\operatorname {LogIntegral}(t)} \left (\int _1^t\frac {e^{\operatorname {LogIntegral}(K[1])} \cot (K[1])}{\log (K[1])}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + log(t)*Derivative(y(t), t) - 1/tan(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out