Internal problem ID [14519]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y=8 \,{\mathrm e}^{2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(t),t$2)+y(t)=8*exp(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} +\frac {8 \,{\mathrm e}^{2 t}}{5} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 25
DSolve[y''[t]+y[t]==8*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {8 e^{2 t}}{5}+c_1 \cos (t)+c_2 \sin (t) \]