74.12.21 problem 21

Internal problem ID [16328]
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 : 21
Date solved : Tuesday, January 28, 2025 at 09:04:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 23

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

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