10.3.1 problem 1

Internal problem ID [1166]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 1
Date solved : Saturday, March 29, 2025 at 10:44:08 PM
CAS classification : [_linear]

\begin{align*} \ln \left (t \right ) y+\left (-3+t \right ) y^{\prime }&=2 t \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 57

ode:=ln(t)*y(t)+(-3+t)*diff(y(t),t) = 2*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{\ln \left (3\right )^{2}+\operatorname {dilog}\left (\frac {t}{3}\right )} \left (-t +3\right )^{-\ln \left (3\right )} \left (-2 \int t \left (-t +3\right )^{-1+\ln \left (3\right )} {\mathrm e}^{-\ln \left (3\right )^{2}-\operatorname {dilog}\left (\frac {t}{3}\right )}d t +c_1 \right ) \]

✓ Mathematica. Time used: 0.178 (sec). Leaf size: 69

ode=Log[t]*y[t]+(-3+t)*D[y[t],t] == 2*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{\operatorname {PolyLog}\left (2,1-\frac {t}{3}\right )-\log (3) \log (t-3)} \left (\int _1^t\frac {2 e^{\log (3) \log (K[1]-3)-\operatorname {PolyLog}\left (2,1-\frac {K[1]}{3}\right )} K[1]}{K[1]-3}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t + (t - 3)*Derivative(y(t), t) + y(t)*log(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out