74.12.25 problem 25

Internal problem ID [16332]
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 : 25
Date solved : Tuesday, January 28, 2025 at 09:04:56 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left ({\mathrm e}^{t}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=cos(exp(t)),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.100 (sec). Leaf size: 61

DSolve[D[y[t],{t,2}]+3*D[y[t],t]+2*y[t]==Cos[Exp[t]],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t} \left (\int _1^t-e^{2 K[1]} \cos \left (e^{K[1]}\right )dK[1]+e^t \int _1^te^{K[2]} \cos \left (e^{K[2]}\right )dK[2]+c_2 e^t+c_1\right ) \]