Internal problem ID [11465]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations:
Undetermined Coefficients. Exercises page 110
Problem number: 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime }-x^{\prime }=6+{\mathrm e}^{2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(x(t),t$2)-diff(x(t),t)=6+exp(2*t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}+\frac {{\mathrm e}^{2 t}}{2}-6 t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 26
DSolve[x''[t]-x'[t]==6+Exp[2*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -6 t+\frac {e^{2 t}}{2}+c_1 e^t+c_2 \]