74.18.43 problem 49

Internal problem ID [16600]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 49
Date solved : Tuesday, January 28, 2025 at 09:12:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve(diff(y(t),t$2)-8*diff(y(t),t)+16*y(t)=1/t^3*exp(4*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 t} \left (2 c_{1} t^{2}+2 c_{2} t +1\right )}{2 t} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 31

DSolve[D[y[t],{t,2}]-8*D[y[t],t]+16*y[t]==1/t^3*Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{4 t} \left (2 c_2 t^2+2 c_1 t+1\right )}{2 t} \]