74.12.28 problem 28

Internal problem ID [16335]
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 : 28
Date solved : Tuesday, January 28, 2025 at 09:05:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

dsolve(diff(y(t),t$2)-10*diff(y(t),t)+25*y(t)=exp(5*t)*ln(2*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{5 t} \left (2 t^{2} \ln \left (2\right )+2 \ln \left (t \right ) t^{2}+4 c_{1} t -3 t^{2}+4 c_{2} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 38

DSolve[D[y[t],{t,2}]-10*D[y[t],t]+25*y[t]==Exp[5*t]*Log[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} e^{5 t} \left (-3 t^2+2 t^2 \log (2 t)+4 c_2 t+4 c_1\right ) \]