Internal problem ID [10449]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }-3 x^{\prime }-4 x-2 t^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(x(t),t$2)-3*diff(x(t),t)-4*x(t)=2*t^2,x(t), singsol=all)
\[ x \left (t \right ) = c_{2} {\mathrm e}^{-t}+{\mathrm e}^{4 t} c_{1} -\frac {t^{2}}{2}+\frac {3 t}{4}-\frac {13}{16} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[x''[t]-3*x'[t]-4*x[t]==2*t^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} (3-2 t) t+c_1 e^{-t}+c_2 e^{4 t}-\frac {13}{16} \\ \end{align*}