74.12.29 problem 29

Internal problem ID [16336]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 09:05:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \arctan \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 38

dsolve(diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=exp(2*t)*arctan(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 42

DSolve[D[y[t],{t,2}]-4*D[y[t],t]+4*y[t]==Exp[2*t]*ArcTan[t],y[t],t,IncludeSingularSolutions -> True]
 

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