67.5.4 problem Problem 1(d)

Internal problem ID [14019]
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(d)
Date solved : Monday, March 31, 2025 at 08:22:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+t*D[y[t],t]-y[t]*Log[t]==Cos[2*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*Derivative(y(t), t) - y(t)*log(t) - cos(2*t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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