74.12.20 problem 20

Internal problem ID [16327]
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 : 20
Date solved : Tuesday, January 28, 2025 at 09:04:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 22

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

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