Internal problem ID [14543]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=-32 t^{2} \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=-32*t^2*cos(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \left (3-4 t \right ) \cos \left (2 t \right )+\left (c_{1} t +c_{2} \right ) {\mathrm e}^{-2 t}-4 t \sin \left (2 t \right ) \left (t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 44
DSolve[y''[t]+4*y'[t]+4*y[t]==-32*t^2*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (3-4 t) \cos (2 t)+e^{-2 t} \left (-4 e^{2 t} (t-1) t \sin (2 t)+c_2 t+c_1\right ) \]