90.25.12 problem 12

Internal problem ID [25393]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 379
Problem number : 12
Date solved : Friday, October 03, 2025 at 12:00:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 26

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+4*y(t) = exp(2*t)/(t^2+1); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{2 t} \left (c_2 +t c_1 -\frac {\ln \left (t^{2}+1\right )}{2}+\arctan \left (t \right ) t \right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 37

ode=D[y[t],{t,2}]-4*D[y[t],t]+4*y[t]==Exp[2*t]/(1+t^2); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{2} e^{2 t} \left (2 t \arctan (t)-\log \left (t^2+1\right )+2 (c_2 t+c_1)\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - exp(2*t)/(t**2 + 1),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(t), t) - (4*t**2*y(t) + t**2*Derivative(y(t), (t, 2