Internal problem ID [11719]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 14, Inhomogeneous second order linear equations. Exercises page
140
Problem number: 14.1 (xi).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+4 x^{\prime }+4 x={\mathrm e}^{2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=exp(2*t),x(t), singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{2 t}}{16}+c_{1} t \,{\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 28
DSolve[x''[t]+4*x'[t]+4*x[t]==Exp[2*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {e^{2 t}}{16}+e^{-2 t} (c_2 t+c_1) \]