Internal problem ID [14528]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=3 t \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$2)+4*y(t)=3*t*exp(-t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} +\frac {3 \left (5 t +2\right ) {\mathrm e}^{-t}}{25} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 34
DSolve[y''[t]+4*y[t]==3*t*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3}{25} e^{-t} (5 t+2)+c_1 \cos (2 t)+c_2 \sin (2 t) \]