Internal problem ID [14600]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\cos \left ({\mathrm e}^{t}\right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = -\left (-c_{2} {\mathrm e}^{t}+\cos \left ({\mathrm e}^{t}\right )+c_{1} +1\right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 26
DSolve[y''[t]+3*y'[t]+2*y[t]==Cos[Exp[t]],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-2 t} \left (-\cos \left (e^t\right )+c_2 e^t+c_1\right ) \]