Internal problem ID [14599]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y={\mathrm e}^{-3 t} \ln \left (t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)+6*diff(y(t),t)+9*y(t)=exp(-3*t)*ln(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-3 t} \left (2 \ln \left (t \right ) t^{2}+4 c_{1} t -3 t^{2}+4 c_{2} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 36
DSolve[y''[t]+6*y'[t]+9*y[t]==Exp[-3*t]*Log[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-3 t} \left (-3 t^2+2 t^2 \log (t)+4 c_2 t+4 c_1\right ) \]