67.5.2 problem Problem 1(b)

Internal problem ID [14017]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 1(b)
Date solved : Monday, March 31, 2025 at 08:22:07 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y&=\ln \left (t \right ) \end{align*}

✗ Maple

ode:=t^2*diff(diff(y(t),t),t)-6*t*diff(y(t),t)+sin(2*t)*y(t) = ln(t); 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=t^2*D[y[t],{t,2}]-6*t*D[y[t],t]+Sin[2*t]*y[t]==Log[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 6*t*Derivative(y(t), t) + y(t)*sin(2*t) - log(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(t), t) - (t**2*Derivative(y(t), (t, 2)) + y(t)*sin(2*t) - log(t))/(6*t) cannot be solved by the factorable group method