Internal problem ID [11720]
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: 14.2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x^{\prime }-2 x=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(x(t),t$2)+diff(x(t),t)-2*x(t)=12*exp(-t)-6*exp(t),x(t), singsol=all)
\[ x \left (t \right ) = c_{2} {\mathrm e}^{-2 t}+c_{1} {\mathrm e}^{t}-6 \,{\mathrm e}^{-t}-2 t \,{\mathrm e}^{t}+\frac {2 \,{\mathrm e}^{t}}{3} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 34
DSolve[x''[t]+x'[t]-2*x[t]==12*Exp[-t]-6*Exp[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-2 t} \left (-6 e^t+e^{3 t} \left (-2 t+\frac {2}{3}+c_2\right )+c_1\right ) \]